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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.analysis.differentiation;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import java.util.ArrayList;<a name="line.19"></a>
<FONT color="green">020</FONT>    import java.util.Arrays;<a name="line.20"></a>
<FONT color="green">021</FONT>    import java.util.List;<a name="line.21"></a>
<FONT color="green">022</FONT>    import java.util.concurrent.atomic.AtomicReference;<a name="line.22"></a>
<FONT color="green">023</FONT>    <a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.exception.DimensionMismatchException;<a name="line.24"></a>
<FONT color="green">025</FONT>    import org.apache.commons.math3.exception.NumberIsTooLargeException;<a name="line.25"></a>
<FONT color="green">026</FONT>    import org.apache.commons.math3.util.ArithmeticUtils;<a name="line.26"></a>
<FONT color="green">027</FONT>    import org.apache.commons.math3.util.FastMath;<a name="line.27"></a>
<FONT color="green">028</FONT>    import org.apache.commons.math3.util.MathArrays;<a name="line.28"></a>
<FONT color="green">029</FONT>    <a name="line.29"></a>
<FONT color="green">030</FONT>    /** Class holding "compiled" computation rules for derivative structures.<a name="line.30"></a>
<FONT color="green">031</FONT>     * &lt;p&gt;This class implements the computation rules described in Dan Kalman's paper &lt;a<a name="line.31"></a>
<FONT color="green">032</FONT>     * href="http://www.math.american.edu/People/kalman/pdffiles/mmgautodiff.pdf"&gt;Doubly<a name="line.32"></a>
<FONT color="green">033</FONT>     * Recursive Multivariate Automatic Differentiation&lt;/a&gt;, Mathematics Magazine, vol. 75,<a name="line.33"></a>
<FONT color="green">034</FONT>     * no. 3, June 2002. However, in order to avoid performances bottlenecks, the recursive<a name="line.34"></a>
<FONT color="green">035</FONT>     * rules are "compiled" once in an unfold form. This class does this recursion unrolling<a name="line.35"></a>
<FONT color="green">036</FONT>     * and stores the computation rules as simple loops with pre-computed indirection arrays.&lt;/p&gt;<a name="line.36"></a>
<FONT color="green">037</FONT>     * &lt;p&gt;<a name="line.37"></a>
<FONT color="green">038</FONT>     * This class maps all derivative computation into single dimension arrays that hold the<a name="line.38"></a>
<FONT color="green">039</FONT>     * value and partial derivatives. The class does not hold these arrays, which remains under<a name="line.39"></a>
<FONT color="green">040</FONT>     * the responsibility of the caller. For each combination of number of free parameters and<a name="line.40"></a>
<FONT color="green">041</FONT>     * derivation order, only one compiler is necessary, and this compiler will be used to<a name="line.41"></a>
<FONT color="green">042</FONT>     * perform computations on all arrays provided to it, which can represent hundreds or<a name="line.42"></a>
<FONT color="green">043</FONT>     * thousands of different parameters kept together with all theur partial derivatives.<a name="line.43"></a>
<FONT color="green">044</FONT>     * &lt;/p&gt;<a name="line.44"></a>
<FONT color="green">045</FONT>     * &lt;p&gt;<a name="line.45"></a>
<FONT color="green">046</FONT>     * The arrays on which compilers operate contain only the partial derivatives together<a name="line.46"></a>
<FONT color="green">047</FONT>     * with the 0&lt;sup&gt;th&lt;/sup&gt; derivative, i.e. the value. The partial derivatives are stored in<a name="line.47"></a>
<FONT color="green">048</FONT>     * a compiler-specific order, which can be retrieved using methods {@link<a name="line.48"></a>
<FONT color="green">049</FONT>     * #getPartialDerivativeIndex(int...) getPartialDerivativeIndex} and {@link<a name="line.49"></a>
<FONT color="green">050</FONT>     * #getPartialDerivativeOrders(int)}. The value is guaranteed to be stored as the first element<a name="line.50"></a>
<FONT color="green">051</FONT>     * (i.e. the {@link #getPartialDerivativeIndex(int...) getPartialDerivativeIndex} method returns<a name="line.51"></a>
<FONT color="green">052</FONT>     * 0 when called with 0 for all derivation orders and {@link #getPartialDerivativeOrders(int)<a name="line.52"></a>
<FONT color="green">053</FONT>     * getPartialDerivativeOrders} returns an array filled with 0 when called with 0 as the index).<a name="line.53"></a>
<FONT color="green">054</FONT>     * &lt;/p&gt;<a name="line.54"></a>
<FONT color="green">055</FONT>     * &lt;p&gt;<a name="line.55"></a>
<FONT color="green">056</FONT>     * Note that the ordering changes with number of parameters and derivation order. For example<a name="line.56"></a>
<FONT color="green">057</FONT>     * given 2 parameters x and y, df/dy is stored at index 2 when derivation order is set to 1 (in<a name="line.57"></a>
<FONT color="green">058</FONT>     * this case the array has three elements: f, df/dx and df/dy). If derivation order is set to<a name="line.58"></a>
<FONT color="green">059</FONT>     * 2, then df/dy will be stored at index 3 (in this case the array has six elements: f, df/dx,<a name="line.59"></a>
<FONT color="green">060</FONT>     * df/dxdx, df/dy, df/dxdy and df/dydy).<a name="line.60"></a>
<FONT color="green">061</FONT>     * &lt;/p&gt;<a name="line.61"></a>
<FONT color="green">062</FONT>     * &lt;p&gt;<a name="line.62"></a>
<FONT color="green">063</FONT>     * Given this structure, users can perform some simple operations like adding, subtracting<a name="line.63"></a>
<FONT color="green">064</FONT>     * or multiplying constants and negating the elements by themselves, knowing if they want to<a name="line.64"></a>
<FONT color="green">065</FONT>     * mutate their array or create a new array. These simple operations are not provided by<a name="line.65"></a>
<FONT color="green">066</FONT>     * the compiler. The compiler provides only the more complex operations between several arrays.<a name="line.66"></a>
<FONT color="green">067</FONT>     * &lt;/p&gt;<a name="line.67"></a>
<FONT color="green">068</FONT>     * &lt;p&gt;This class is mainly used as the engine for scalar variable {@link DerivativeStructure}.<a name="line.68"></a>
<FONT color="green">069</FONT>     * It can also be used directly to hold several variables in arrays for more complex data<a name="line.69"></a>
<FONT color="green">070</FONT>     * structures. User can for example store a vector of n variables depending on three x, y<a name="line.70"></a>
<FONT color="green">071</FONT>     * and z free parameters in one array as follows:<a name="line.71"></a>
<FONT color="green">072</FONT>     * &lt;pre&gt;<a name="line.72"></a>
<FONT color="green">073</FONT>     *   // parameter 0 is x, parameter 1 is y, parameter 2 is z<a name="line.73"></a>
<FONT color="green">074</FONT>     *   int parameters = 3;<a name="line.74"></a>
<FONT color="green">075</FONT>     *   DSCompiler compiler = DSCompiler.getCompiler(parameters, order);<a name="line.75"></a>
<FONT color="green">076</FONT>     *   int size = compiler.getSize();<a name="line.76"></a>
<FONT color="green">077</FONT>     *<a name="line.77"></a>
<FONT color="green">078</FONT>     *   // pack all elements in a single array<a name="line.78"></a>
<FONT color="green">079</FONT>     *   double[] array = new double[n * size];<a name="line.79"></a>
<FONT color="green">080</FONT>     *   for (int i = 0; i &lt; n; ++i) {<a name="line.80"></a>
<FONT color="green">081</FONT>     *<a name="line.81"></a>
<FONT color="green">082</FONT>     *     // we know value is guaranteed to be the first element<a name="line.82"></a>
<FONT color="green">083</FONT>     *     array[i * size] = v[i];<a name="line.83"></a>
<FONT color="green">084</FONT>     *<a name="line.84"></a>
<FONT color="green">085</FONT>     *     // we don't know where first derivatives are stored, so we ask the compiler<a name="line.85"></a>
<FONT color="green">086</FONT>     *     array[i * size + compiler.getPartialDerivativeIndex(1, 0, 0) = dvOnDx[i][0];<a name="line.86"></a>
<FONT color="green">087</FONT>     *     array[i * size + compiler.getPartialDerivativeIndex(0, 1, 0) = dvOnDy[i][0];<a name="line.87"></a>
<FONT color="green">088</FONT>     *     array[i * size + compiler.getPartialDerivativeIndex(0, 0, 1) = dvOnDz[i][0];<a name="line.88"></a>
<FONT color="green">089</FONT>     *<a name="line.89"></a>
<FONT color="green">090</FONT>     *     // we let all higher order derivatives set to 0<a name="line.90"></a>
<FONT color="green">091</FONT>     *<a name="line.91"></a>
<FONT color="green">092</FONT>     *   }<a name="line.92"></a>
<FONT color="green">093</FONT>     * &lt;/pre&gt;<a name="line.93"></a>
<FONT color="green">094</FONT>     * Then in another function, user can perform some operations on all elements stored<a name="line.94"></a>
<FONT color="green">095</FONT>     * in the single array, such as a simple product of all variables:<a name="line.95"></a>
<FONT color="green">096</FONT>     * &lt;pre&gt;<a name="line.96"></a>
<FONT color="green">097</FONT>     *   // compute the product of all elements<a name="line.97"></a>
<FONT color="green">098</FONT>     *   double[] product = new double[size];<a name="line.98"></a>
<FONT color="green">099</FONT>     *   prod[0] = 1.0;<a name="line.99"></a>
<FONT color="green">100</FONT>     *   for (int i = 0; i &lt; n; ++i) {<a name="line.100"></a>
<FONT color="green">101</FONT>     *     double[] tmp = product.clone();<a name="line.101"></a>
<FONT color="green">102</FONT>     *     compiler.multiply(tmp, 0, array, i * size, product, 0);<a name="line.102"></a>
<FONT color="green">103</FONT>     *   }<a name="line.103"></a>
<FONT color="green">104</FONT>     *<a name="line.104"></a>
<FONT color="green">105</FONT>     *   // value<a name="line.105"></a>
<FONT color="green">106</FONT>     *   double p = product[0];<a name="line.106"></a>
<FONT color="green">107</FONT>     *<a name="line.107"></a>
<FONT color="green">108</FONT>     *   // first derivatives<a name="line.108"></a>
<FONT color="green">109</FONT>     *   double dPdX = product[compiler.getPartialDerivativeIndex(1, 0, 0)];<a name="line.109"></a>
<FONT color="green">110</FONT>     *   double dPdY = product[compiler.getPartialDerivativeIndex(0, 1, 0)];<a name="line.110"></a>
<FONT color="green">111</FONT>     *   double dPdZ = product[compiler.getPartialDerivativeIndex(0, 0, 1)];<a name="line.111"></a>
<FONT color="green">112</FONT>     *<a name="line.112"></a>
<FONT color="green">113</FONT>     *   // cross derivatives (assuming order was at least 2)<a name="line.113"></a>
<FONT color="green">114</FONT>     *   double dPdXdX = product[compiler.getPartialDerivativeIndex(2, 0, 0)];<a name="line.114"></a>
<FONT color="green">115</FONT>     *   double dPdXdY = product[compiler.getPartialDerivativeIndex(1, 1, 0)];<a name="line.115"></a>
<FONT color="green">116</FONT>     *   double dPdXdZ = product[compiler.getPartialDerivativeIndex(1, 0, 1)];<a name="line.116"></a>
<FONT color="green">117</FONT>     *   double dPdYdY = product[compiler.getPartialDerivativeIndex(0, 2, 0)];<a name="line.117"></a>
<FONT color="green">118</FONT>     *   double dPdYdZ = product[compiler.getPartialDerivativeIndex(0, 1, 1)];<a name="line.118"></a>
<FONT color="green">119</FONT>     *   double dPdZdZ = product[compiler.getPartialDerivativeIndex(0, 0, 2)];<a name="line.119"></a>
<FONT color="green">120</FONT>     * &lt;/p&gt;<a name="line.120"></a>
<FONT color="green">121</FONT>     * @see DerivativeStructure<a name="line.121"></a>
<FONT color="green">122</FONT>     * @version $Id: DSCompiler.java 1421949 2012-12-14 15:53:32Z luc $<a name="line.122"></a>
<FONT color="green">123</FONT>     * @since 3.1<a name="line.123"></a>
<FONT color="green">124</FONT>     */<a name="line.124"></a>
<FONT color="green">125</FONT>    public class DSCompiler {<a name="line.125"></a>
<FONT color="green">126</FONT>    <a name="line.126"></a>
<FONT color="green">127</FONT>        /** Array of all compilers created so far. */<a name="line.127"></a>
<FONT color="green">128</FONT>        private static AtomicReference&lt;DSCompiler[][]&gt; compilers =<a name="line.128"></a>
<FONT color="green">129</FONT>                new AtomicReference&lt;DSCompiler[][]&gt;(null);<a name="line.129"></a>
<FONT color="green">130</FONT>    <a name="line.130"></a>
<FONT color="green">131</FONT>        /** Number of free parameters. */<a name="line.131"></a>
<FONT color="green">132</FONT>        private final int parameters;<a name="line.132"></a>
<FONT color="green">133</FONT>    <a name="line.133"></a>
<FONT color="green">134</FONT>        /** Derivation order. */<a name="line.134"></a>
<FONT color="green">135</FONT>        private final int order;<a name="line.135"></a>
<FONT color="green">136</FONT>    <a name="line.136"></a>
<FONT color="green">137</FONT>        /** Number of partial derivatives (including the single 0 order derivative element). */<a name="line.137"></a>
<FONT color="green">138</FONT>        private final int[][] sizes;<a name="line.138"></a>
<FONT color="green">139</FONT>    <a name="line.139"></a>
<FONT color="green">140</FONT>        /** Indirection array for partial derivatives. */<a name="line.140"></a>
<FONT color="green">141</FONT>        private final int[][] derivativesIndirection;<a name="line.141"></a>
<FONT color="green">142</FONT>    <a name="line.142"></a>
<FONT color="green">143</FONT>        /** Indirection array of the lower derivative elements. */<a name="line.143"></a>
<FONT color="green">144</FONT>        private final int[] lowerIndirection;<a name="line.144"></a>
<FONT color="green">145</FONT>    <a name="line.145"></a>
<FONT color="green">146</FONT>        /** Indirection arrays for multiplication. */<a name="line.146"></a>
<FONT color="green">147</FONT>        private final int[][][] multIndirection;<a name="line.147"></a>
<FONT color="green">148</FONT>    <a name="line.148"></a>
<FONT color="green">149</FONT>        /** Indirection arrays for function composition. */<a name="line.149"></a>
<FONT color="green">150</FONT>        private final int[][][] compIndirection;<a name="line.150"></a>
<FONT color="green">151</FONT>    <a name="line.151"></a>
<FONT color="green">152</FONT>        /** Private constructor, reserved for the factory method {@link #getCompiler(int, int)}.<a name="line.152"></a>
<FONT color="green">153</FONT>         * @param parameters number of free parameters<a name="line.153"></a>
<FONT color="green">154</FONT>         * @param order derivation order<a name="line.154"></a>
<FONT color="green">155</FONT>         * @param valueCompiler compiler for the value part<a name="line.155"></a>
<FONT color="green">156</FONT>         * @param derivativeCompiler compiler for the derivative part<a name="line.156"></a>
<FONT color="green">157</FONT>         */<a name="line.157"></a>
<FONT color="green">158</FONT>        private DSCompiler(final int parameters, final int order,<a name="line.158"></a>
<FONT color="green">159</FONT>                           final DSCompiler valueCompiler, final DSCompiler derivativeCompiler) {<a name="line.159"></a>
<FONT color="green">160</FONT>    <a name="line.160"></a>
<FONT color="green">161</FONT>            this.parameters = parameters;<a name="line.161"></a>
<FONT color="green">162</FONT>            this.order      = order;<a name="line.162"></a>
<FONT color="green">163</FONT>            this.sizes      = compileSizes(parameters, order, valueCompiler);<a name="line.163"></a>
<FONT color="green">164</FONT>            this.derivativesIndirection =<a name="line.164"></a>
<FONT color="green">165</FONT>                    compileDerivativesIndirection(parameters, order,<a name="line.165"></a>
<FONT color="green">166</FONT>                                                  valueCompiler, derivativeCompiler);<a name="line.166"></a>
<FONT color="green">167</FONT>            this.lowerIndirection =<a name="line.167"></a>
<FONT color="green">168</FONT>                    compileLowerIndirection(parameters, order,<a name="line.168"></a>
<FONT color="green">169</FONT>                                            valueCompiler, derivativeCompiler);<a name="line.169"></a>
<FONT color="green">170</FONT>            this.multIndirection =<a name="line.170"></a>
<FONT color="green">171</FONT>                    compileMultiplicationIndirection(parameters, order,<a name="line.171"></a>
<FONT color="green">172</FONT>                                                     valueCompiler, derivativeCompiler, lowerIndirection);<a name="line.172"></a>
<FONT color="green">173</FONT>            this.compIndirection =<a name="line.173"></a>
<FONT color="green">174</FONT>                    compileCompositionIndirection(parameters, order,<a name="line.174"></a>
<FONT color="green">175</FONT>                                                  valueCompiler, derivativeCompiler,<a name="line.175"></a>
<FONT color="green">176</FONT>                                                  sizes, derivativesIndirection);<a name="line.176"></a>
<FONT color="green">177</FONT>    <a name="line.177"></a>
<FONT color="green">178</FONT>        }<a name="line.178"></a>
<FONT color="green">179</FONT>    <a name="line.179"></a>
<FONT color="green">180</FONT>        /** Get the compiler for number of free parameters and order.<a name="line.180"></a>
<FONT color="green">181</FONT>         * @param parameters number of free parameters<a name="line.181"></a>
<FONT color="green">182</FONT>         * @param order derivation order<a name="line.182"></a>
<FONT color="green">183</FONT>         * @return cached rules set<a name="line.183"></a>
<FONT color="green">184</FONT>         */<a name="line.184"></a>
<FONT color="green">185</FONT>        public static DSCompiler getCompiler(int parameters, int order) {<a name="line.185"></a>
<FONT color="green">186</FONT>    <a name="line.186"></a>
<FONT color="green">187</FONT>            // get the cached compilers<a name="line.187"></a>
<FONT color="green">188</FONT>            final DSCompiler[][] cache = compilers.get();<a name="line.188"></a>
<FONT color="green">189</FONT>            if (cache != null &amp;&amp; cache.length &gt; parameters &amp;&amp; cache[parameters].length &gt; order) {<a name="line.189"></a>
<FONT color="green">190</FONT>                if (cache[parameters][order] != null) {<a name="line.190"></a>
<FONT color="green">191</FONT>                    // the compiler has already been created<a name="line.191"></a>
<FONT color="green">192</FONT>                    return cache[parameters][order];<a name="line.192"></a>
<FONT color="green">193</FONT>                }<a name="line.193"></a>
<FONT color="green">194</FONT>            }<a name="line.194"></a>
<FONT color="green">195</FONT>    <a name="line.195"></a>
<FONT color="green">196</FONT>            // we need to create more compilers<a name="line.196"></a>
<FONT color="green">197</FONT>            final int maxParameters = FastMath.max(parameters, cache == null ? 0 : cache.length);<a name="line.197"></a>
<FONT color="green">198</FONT>            final int maxOrder      = FastMath.max(order,     cache == null ? 0 : cache[0].length);<a name="line.198"></a>
<FONT color="green">199</FONT>            final DSCompiler[][] newCache = new DSCompiler[maxParameters + 1][maxOrder + 1];<a name="line.199"></a>
<FONT color="green">200</FONT>    <a name="line.200"></a>
<FONT color="green">201</FONT>            if (cache != null) {<a name="line.201"></a>
<FONT color="green">202</FONT>                // preserve the already created compilers<a name="line.202"></a>
<FONT color="green">203</FONT>                for (int i = 0; i &lt; cache.length; ++i) {<a name="line.203"></a>
<FONT color="green">204</FONT>                    System.arraycopy(cache[i], 0, newCache[i], 0, cache[i].length);<a name="line.204"></a>
<FONT color="green">205</FONT>                }<a name="line.205"></a>
<FONT color="green">206</FONT>            }<a name="line.206"></a>
<FONT color="green">207</FONT>    <a name="line.207"></a>
<FONT color="green">208</FONT>            // create the array in increasing diagonal order<a name="line.208"></a>
<FONT color="green">209</FONT>            for (int diag = 0; diag &lt;= parameters + order; ++diag) {<a name="line.209"></a>
<FONT color="green">210</FONT>                for (int o = FastMath.max(0, diag - parameters); o &lt;= FastMath.min(order, diag); ++o) {<a name="line.210"></a>
<FONT color="green">211</FONT>                    final int p = diag - o;<a name="line.211"></a>
<FONT color="green">212</FONT>                    if (newCache[p][o] == null) {<a name="line.212"></a>
<FONT color="green">213</FONT>                        final DSCompiler valueCompiler      = (p == 0) ? null : newCache[p - 1][o];<a name="line.213"></a>
<FONT color="green">214</FONT>                        final DSCompiler derivativeCompiler = (o == 0) ? null : newCache[p][o - 1];<a name="line.214"></a>
<FONT color="green">215</FONT>                        newCache[p][o] = new DSCompiler(p, o, valueCompiler, derivativeCompiler);<a name="line.215"></a>
<FONT color="green">216</FONT>                    }<a name="line.216"></a>
<FONT color="green">217</FONT>                }<a name="line.217"></a>
<FONT color="green">218</FONT>            }<a name="line.218"></a>
<FONT color="green">219</FONT>    <a name="line.219"></a>
<FONT color="green">220</FONT>            // atomically reset the cached compilers array<a name="line.220"></a>
<FONT color="green">221</FONT>            compilers.compareAndSet(cache, newCache);<a name="line.221"></a>
<FONT color="green">222</FONT>    <a name="line.222"></a>
<FONT color="green">223</FONT>            return newCache[parameters][order];<a name="line.223"></a>
<FONT color="green">224</FONT>    <a name="line.224"></a>
<FONT color="green">225</FONT>        }<a name="line.225"></a>
<FONT color="green">226</FONT>    <a name="line.226"></a>
<FONT color="green">227</FONT>        /** Compile the sizes array.<a name="line.227"></a>
<FONT color="green">228</FONT>         * @param parameters number of free parameters<a name="line.228"></a>
<FONT color="green">229</FONT>         * @param order derivation order<a name="line.229"></a>
<FONT color="green">230</FONT>         * @param valueCompiler compiler for the value part<a name="line.230"></a>
<FONT color="green">231</FONT>         * @return sizes array<a name="line.231"></a>
<FONT color="green">232</FONT>         */<a name="line.232"></a>
<FONT color="green">233</FONT>        private static int[][] compileSizes(final int parameters, final int order,<a name="line.233"></a>
<FONT color="green">234</FONT>                                            final DSCompiler valueCompiler) {<a name="line.234"></a>
<FONT color="green">235</FONT>    <a name="line.235"></a>
<FONT color="green">236</FONT>            final int[][] sizes = new int[parameters + 1][order + 1];<a name="line.236"></a>
<FONT color="green">237</FONT>            if (parameters == 0) {<a name="line.237"></a>
<FONT color="green">238</FONT>                Arrays.fill(sizes[0], 1);<a name="line.238"></a>
<FONT color="green">239</FONT>            } else {<a name="line.239"></a>
<FONT color="green">240</FONT>                System.arraycopy(valueCompiler.sizes, 0, sizes, 0, parameters);<a name="line.240"></a>
<FONT color="green">241</FONT>                sizes[parameters][0] = 1;<a name="line.241"></a>
<FONT color="green">242</FONT>                for (int i = 0; i &lt; order; ++i) {<a name="line.242"></a>
<FONT color="green">243</FONT>                    sizes[parameters][i + 1] = sizes[parameters][i] + sizes[parameters - 1][i + 1];<a name="line.243"></a>
<FONT color="green">244</FONT>                }<a name="line.244"></a>
<FONT color="green">245</FONT>            }<a name="line.245"></a>
<FONT color="green">246</FONT>    <a name="line.246"></a>
<FONT color="green">247</FONT>            return sizes;<a name="line.247"></a>
<FONT color="green">248</FONT>    <a name="line.248"></a>
<FONT color="green">249</FONT>        }<a name="line.249"></a>
<FONT color="green">250</FONT>    <a name="line.250"></a>
<FONT color="green">251</FONT>        /** Compile the derivatives indirection array.<a name="line.251"></a>
<FONT color="green">252</FONT>         * @param parameters number of free parameters<a name="line.252"></a>
<FONT color="green">253</FONT>         * @param order derivation order<a name="line.253"></a>
<FONT color="green">254</FONT>         * @param valueCompiler compiler for the value part<a name="line.254"></a>
<FONT color="green">255</FONT>         * @param derivativeCompiler compiler for the derivative part<a name="line.255"></a>
<FONT color="green">256</FONT>         * @return derivatives indirection array<a name="line.256"></a>
<FONT color="green">257</FONT>         */<a name="line.257"></a>
<FONT color="green">258</FONT>        private static int[][] compileDerivativesIndirection(final int parameters, final int order,<a name="line.258"></a>
<FONT color="green">259</FONT>                                                          final DSCompiler valueCompiler,<a name="line.259"></a>
<FONT color="green">260</FONT>                                                          final DSCompiler derivativeCompiler) {<a name="line.260"></a>
<FONT color="green">261</FONT>    <a name="line.261"></a>
<FONT color="green">262</FONT>            if (parameters == 0 || order == 0) {<a name="line.262"></a>
<FONT color="green">263</FONT>                return new int[1][parameters];<a name="line.263"></a>
<FONT color="green">264</FONT>            }<a name="line.264"></a>
<FONT color="green">265</FONT>    <a name="line.265"></a>
<FONT color="green">266</FONT>            final int vSize = valueCompiler.derivativesIndirection.length;<a name="line.266"></a>
<FONT color="green">267</FONT>            final int dSize = derivativeCompiler.derivativesIndirection.length;<a name="line.267"></a>
<FONT color="green">268</FONT>            final int[][] derivativesIndirection = new int[vSize + dSize][parameters];<a name="line.268"></a>
<FONT color="green">269</FONT>    <a name="line.269"></a>
<FONT color="green">270</FONT>            // set up the indices for the value part<a name="line.270"></a>
<FONT color="green">271</FONT>            for (int i = 0; i &lt; vSize; ++i) {<a name="line.271"></a>
<FONT color="green">272</FONT>                // copy the first indices, the last one remaining set to 0<a name="line.272"></a>
<FONT color="green">273</FONT>                System.arraycopy(valueCompiler.derivativesIndirection[i], 0,<a name="line.273"></a>
<FONT color="green">274</FONT>                                 derivativesIndirection[i], 0,<a name="line.274"></a>
<FONT color="green">275</FONT>                                 parameters - 1);<a name="line.275"></a>
<FONT color="green">276</FONT>            }<a name="line.276"></a>
<FONT color="green">277</FONT>    <a name="line.277"></a>
<FONT color="green">278</FONT>            // set up the indices for the derivative part<a name="line.278"></a>
<FONT color="green">279</FONT>            for (int i = 0; i &lt; dSize; ++i) {<a name="line.279"></a>
<FONT color="green">280</FONT>    <a name="line.280"></a>
<FONT color="green">281</FONT>                // copy the indices<a name="line.281"></a>
<FONT color="green">282</FONT>                System.arraycopy(derivativeCompiler.derivativesIndirection[i], 0,<a name="line.282"></a>
<FONT color="green">283</FONT>                                 derivativesIndirection[vSize + i], 0,<a name="line.283"></a>
<FONT color="green">284</FONT>                                 parameters);<a name="line.284"></a>
<FONT color="green">285</FONT>    <a name="line.285"></a>
<FONT color="green">286</FONT>                // increment the derivation order for the last parameter<a name="line.286"></a>
<FONT color="green">287</FONT>                derivativesIndirection[vSize + i][parameters - 1]++;<a name="line.287"></a>
<FONT color="green">288</FONT>    <a name="line.288"></a>
<FONT color="green">289</FONT>            }<a name="line.289"></a>
<FONT color="green">290</FONT>    <a name="line.290"></a>
<FONT color="green">291</FONT>            return derivativesIndirection;<a name="line.291"></a>
<FONT color="green">292</FONT>    <a name="line.292"></a>
<FONT color="green">293</FONT>        }<a name="line.293"></a>
<FONT color="green">294</FONT>    <a name="line.294"></a>
<FONT color="green">295</FONT>        /** Compile the lower derivatives indirection array.<a name="line.295"></a>
<FONT color="green">296</FONT>         * &lt;p&gt;<a name="line.296"></a>
<FONT color="green">297</FONT>         * This indirection array contains the indices of all elements<a name="line.297"></a>
<FONT color="green">298</FONT>         * except derivatives for last derivation order.<a name="line.298"></a>
<FONT color="green">299</FONT>         * &lt;/p&gt;<a name="line.299"></a>
<FONT color="green">300</FONT>         * @param parameters number of free parameters<a name="line.300"></a>
<FONT color="green">301</FONT>         * @param order derivation order<a name="line.301"></a>
<FONT color="green">302</FONT>         * @param valueCompiler compiler for the value part<a name="line.302"></a>
<FONT color="green">303</FONT>         * @param derivativeCompiler compiler for the derivative part<a name="line.303"></a>
<FONT color="green">304</FONT>         * @return lower derivatives indirection array<a name="line.304"></a>
<FONT color="green">305</FONT>         */<a name="line.305"></a>
<FONT color="green">306</FONT>        private static int[] compileLowerIndirection(final int parameters, final int order,<a name="line.306"></a>
<FONT color="green">307</FONT>                                                  final DSCompiler valueCompiler,<a name="line.307"></a>
<FONT color="green">308</FONT>                                                  final DSCompiler derivativeCompiler) {<a name="line.308"></a>
<FONT color="green">309</FONT>    <a name="line.309"></a>
<FONT color="green">310</FONT>            if (parameters == 0 || order &lt;= 1) {<a name="line.310"></a>
<FONT color="green">311</FONT>                return new int[] { 0 };<a name="line.311"></a>
<FONT color="green">312</FONT>            }<a name="line.312"></a>
<FONT color="green">313</FONT>    <a name="line.313"></a>
<FONT color="green">314</FONT>            // this is an implementation of definition 6 in Dan Kalman's paper.<a name="line.314"></a>
<FONT color="green">315</FONT>            final int vSize = valueCompiler.lowerIndirection.length;<a name="line.315"></a>
<FONT color="green">316</FONT>            final int dSize = derivativeCompiler.lowerIndirection.length;<a name="line.316"></a>
<FONT color="green">317</FONT>            final int[] lowerIndirection = new int[vSize + dSize];<a name="line.317"></a>
<FONT color="green">318</FONT>            System.arraycopy(valueCompiler.lowerIndirection, 0, lowerIndirection, 0, vSize);<a name="line.318"></a>
<FONT color="green">319</FONT>            for (int i = 0; i &lt; dSize; ++i) {<a name="line.319"></a>
<FONT color="green">320</FONT>                lowerIndirection[vSize + i] = valueCompiler.getSize() + derivativeCompiler.lowerIndirection[i];<a name="line.320"></a>
<FONT color="green">321</FONT>            }<a name="line.321"></a>
<FONT color="green">322</FONT>    <a name="line.322"></a>
<FONT color="green">323</FONT>            return lowerIndirection;<a name="line.323"></a>
<FONT color="green">324</FONT>    <a name="line.324"></a>
<FONT color="green">325</FONT>        }<a name="line.325"></a>
<FONT color="green">326</FONT>    <a name="line.326"></a>
<FONT color="green">327</FONT>        /** Compile the multiplication indirection array.<a name="line.327"></a>
<FONT color="green">328</FONT>         * &lt;p&gt;<a name="line.328"></a>
<FONT color="green">329</FONT>         * This indirection array contains the indices of all pairs of elements<a name="line.329"></a>
<FONT color="green">330</FONT>         * involved when computing a multiplication. This allows a straightforward<a name="line.330"></a>
<FONT color="green">331</FONT>         * loop-based multiplication (see {@link #multiply(double[], int, double[], int, double[], int)}).<a name="line.331"></a>
<FONT color="green">332</FONT>         * &lt;/p&gt;<a name="line.332"></a>
<FONT color="green">333</FONT>         * @param parameters number of free parameters<a name="line.333"></a>
<FONT color="green">334</FONT>         * @param order derivation order<a name="line.334"></a>
<FONT color="green">335</FONT>         * @param valueCompiler compiler for the value part<a name="line.335"></a>
<FONT color="green">336</FONT>         * @param derivativeCompiler compiler for the derivative part<a name="line.336"></a>
<FONT color="green">337</FONT>         * @param lowerIndirection lower derivatives indirection array<a name="line.337"></a>
<FONT color="green">338</FONT>         * @return multiplication indirection array<a name="line.338"></a>
<FONT color="green">339</FONT>         */<a name="line.339"></a>
<FONT color="green">340</FONT>        private static int[][][] compileMultiplicationIndirection(final int parameters, final int order,<a name="line.340"></a>
<FONT color="green">341</FONT>                                                               final DSCompiler valueCompiler,<a name="line.341"></a>
<FONT color="green">342</FONT>                                                               final DSCompiler derivativeCompiler,<a name="line.342"></a>
<FONT color="green">343</FONT>                                                               final int[] lowerIndirection) {<a name="line.343"></a>
<FONT color="green">344</FONT>    <a name="line.344"></a>
<FONT color="green">345</FONT>            if ((parameters == 0) || (order == 0)) {<a name="line.345"></a>
<FONT color="green">346</FONT>                return new int[][][] { { { 1, 0, 0 } } };<a name="line.346"></a>
<FONT color="green">347</FONT>            }<a name="line.347"></a>
<FONT color="green">348</FONT>    <a name="line.348"></a>
<FONT color="green">349</FONT>            // this is an implementation of definition 3 in Dan Kalman's paper.<a name="line.349"></a>
<FONT color="green">350</FONT>            final int vSize = valueCompiler.multIndirection.length;<a name="line.350"></a>
<FONT color="green">351</FONT>            final int dSize = derivativeCompiler.multIndirection.length;<a name="line.351"></a>
<FONT color="green">352</FONT>            final int[][][] multIndirection = new int[vSize + dSize][][];<a name="line.352"></a>
<FONT color="green">353</FONT>    <a name="line.353"></a>
<FONT color="green">354</FONT>            System.arraycopy(valueCompiler.multIndirection, 0, multIndirection, 0, vSize);<a name="line.354"></a>
<FONT color="green">355</FONT>    <a name="line.355"></a>
<FONT color="green">356</FONT>            for (int i = 0; i &lt; dSize; ++i) {<a name="line.356"></a>
<FONT color="green">357</FONT>                final int[][] dRow = derivativeCompiler.multIndirection[i];<a name="line.357"></a>
<FONT color="green">358</FONT>                List&lt;int[]&gt; row = new ArrayList&lt;int[]&gt;();<a name="line.358"></a>
<FONT color="green">359</FONT>                for (int j = 0; j &lt; dRow.length; ++j) {<a name="line.359"></a>
<FONT color="green">360</FONT>                    row.add(new int[] { dRow[j][0], lowerIndirection[dRow[j][1]], vSize + dRow[j][2] });<a name="line.360"></a>
<FONT color="green">361</FONT>                    row.add(new int[] { dRow[j][0], vSize + dRow[j][1], lowerIndirection[dRow[j][2]] });<a name="line.361"></a>
<FONT color="green">362</FONT>                }<a name="line.362"></a>
<FONT color="green">363</FONT>    <a name="line.363"></a>
<FONT color="green">364</FONT>                // combine terms with similar derivation orders<a name="line.364"></a>
<FONT color="green">365</FONT>                final List&lt;int[]&gt; combined = new ArrayList&lt;int[]&gt;(row.size());<a name="line.365"></a>
<FONT color="green">366</FONT>                for (int j = 0; j &lt; row.size(); ++j) {<a name="line.366"></a>
<FONT color="green">367</FONT>                    final int[] termJ = row.get(j);<a name="line.367"></a>
<FONT color="green">368</FONT>                    if (termJ[0] &gt; 0) {<a name="line.368"></a>
<FONT color="green">369</FONT>                        for (int k = j + 1; k &lt; row.size(); ++k) {<a name="line.369"></a>
<FONT color="green">370</FONT>                            final int[] termK = row.get(k);<a name="line.370"></a>
<FONT color="green">371</FONT>                            if (termJ[1] == termK[1] &amp;&amp; termJ[2] == termK[2]) {<a name="line.371"></a>
<FONT color="green">372</FONT>                                // combine termJ and termK<a name="line.372"></a>
<FONT color="green">373</FONT>                                termJ[0] += termK[0];<a name="line.373"></a>
<FONT color="green">374</FONT>                                // make sure we will skip termK later on in the outer loop<a name="line.374"></a>
<FONT color="green">375</FONT>                                termK[0] = 0;<a name="line.375"></a>
<FONT color="green">376</FONT>                            }<a name="line.376"></a>
<FONT color="green">377</FONT>                        }<a name="line.377"></a>
<FONT color="green">378</FONT>                        combined.add(termJ);<a name="line.378"></a>
<FONT color="green">379</FONT>                    }<a name="line.379"></a>
<FONT color="green">380</FONT>                }<a name="line.380"></a>
<FONT color="green">381</FONT>    <a name="line.381"></a>
<FONT color="green">382</FONT>                multIndirection[vSize + i] = combined.toArray(new int[combined.size()][]);<a name="line.382"></a>
<FONT color="green">383</FONT>    <a name="line.383"></a>
<FONT color="green">384</FONT>            }<a name="line.384"></a>
<FONT color="green">385</FONT>    <a name="line.385"></a>
<FONT color="green">386</FONT>            return multIndirection;<a name="line.386"></a>
<FONT color="green">387</FONT>    <a name="line.387"></a>
<FONT color="green">388</FONT>        }<a name="line.388"></a>
<FONT color="green">389</FONT>    <a name="line.389"></a>
<FONT color="green">390</FONT>        /** Compile the function composition indirection array.<a name="line.390"></a>
<FONT color="green">391</FONT>         * &lt;p&gt;<a name="line.391"></a>
<FONT color="green">392</FONT>         * This indirection array contains the indices of all sets of elements<a name="line.392"></a>
<FONT color="green">393</FONT>         * involved when computing a composition. This allows a straightforward<a name="line.393"></a>
<FONT color="green">394</FONT>         * loop-based composition (see {@link #compose(double[], int, double[], double[], int)}).<a name="line.394"></a>
<FONT color="green">395</FONT>         * &lt;/p&gt;<a name="line.395"></a>
<FONT color="green">396</FONT>         * @param parameters number of free parameters<a name="line.396"></a>
<FONT color="green">397</FONT>         * @param order derivation order<a name="line.397"></a>
<FONT color="green">398</FONT>         * @param valueCompiler compiler for the value part<a name="line.398"></a>
<FONT color="green">399</FONT>         * @param derivativeCompiler compiler for the derivative part<a name="line.399"></a>
<FONT color="green">400</FONT>         * @param sizes sizes array<a name="line.400"></a>
<FONT color="green">401</FONT>         * @param derivativesIndirection derivatives indirection array<a name="line.401"></a>
<FONT color="green">402</FONT>         * @return multiplication indirection array<a name="line.402"></a>
<FONT color="green">403</FONT>         */<a name="line.403"></a>
<FONT color="green">404</FONT>        private static int[][][] compileCompositionIndirection(final int parameters, final int order,<a name="line.404"></a>
<FONT color="green">405</FONT>                                                            final DSCompiler valueCompiler,<a name="line.405"></a>
<FONT color="green">406</FONT>                                                            final DSCompiler derivativeCompiler,<a name="line.406"></a>
<FONT color="green">407</FONT>                                                            final int[][] sizes,<a name="line.407"></a>
<FONT color="green">408</FONT>                                                            final int[][] derivativesIndirection) {<a name="line.408"></a>
<FONT color="green">409</FONT>    <a name="line.409"></a>
<FONT color="green">410</FONT>            if ((parameters == 0) || (order == 0)) {<a name="line.410"></a>
<FONT color="green">411</FONT>                return new int[][][] { { { 1, 0 } } };<a name="line.411"></a>
<FONT color="green">412</FONT>            }<a name="line.412"></a>
<FONT color="green">413</FONT>    <a name="line.413"></a>
<FONT color="green">414</FONT>            final int vSize = valueCompiler.compIndirection.length;<a name="line.414"></a>
<FONT color="green">415</FONT>            final int dSize = derivativeCompiler.compIndirection.length;<a name="line.415"></a>
<FONT color="green">416</FONT>            final int[][][] compIndirection = new int[vSize + dSize][][];<a name="line.416"></a>
<FONT color="green">417</FONT>    <a name="line.417"></a>
<FONT color="green">418</FONT>            // the composition rules from the value part can be reused as is<a name="line.418"></a>
<FONT color="green">419</FONT>            System.arraycopy(valueCompiler.compIndirection, 0, compIndirection, 0, vSize);<a name="line.419"></a>
<FONT color="green">420</FONT>    <a name="line.420"></a>
<FONT color="green">421</FONT>            // the composition rules for the derivative part are deduced by<a name="line.421"></a>
<FONT color="green">422</FONT>            // differentiation the rules from the underlying compiler once<a name="line.422"></a>
<FONT color="green">423</FONT>            // with respect to the parameter this compiler handles and the<a name="line.423"></a>
<FONT color="green">424</FONT>            // underlying one did not handle<a name="line.424"></a>
<FONT color="green">425</FONT>            for (int i = 0; i &lt; dSize; ++i) {<a name="line.425"></a>
<FONT color="green">426</FONT>                List&lt;int[]&gt; row = new ArrayList&lt;int[]&gt;();<a name="line.426"></a>
<FONT color="green">427</FONT>                for (int[] term : derivativeCompiler.compIndirection[i]) {<a name="line.427"></a>
<FONT color="green">428</FONT>    <a name="line.428"></a>
<FONT color="green">429</FONT>                    // handle term p * f_k(g(x)) * g_l1(x) * g_l2(x) * ... * g_lp(x)<a name="line.429"></a>
<FONT color="green">430</FONT>    <a name="line.430"></a>
<FONT color="green">431</FONT>                    // derive the first factor in the term: f_k with respect to new parameter<a name="line.431"></a>
<FONT color="green">432</FONT>                    int[] derivedTermF = new int[term.length + 1];<a name="line.432"></a>
<FONT color="green">433</FONT>                    derivedTermF[0] = term[0];     // p<a name="line.433"></a>
<FONT color="green">434</FONT>                    derivedTermF[1] = term[1] + 1; // f_(k+1)<a name="line.434"></a>
<FONT color="green">435</FONT>                    int[] orders = new int[parameters];<a name="line.435"></a>
<FONT color="green">436</FONT>                    orders[parameters - 1] = 1;<a name="line.436"></a>
<FONT color="green">437</FONT>                    derivedTermF[term.length] = getPartialDerivativeIndex(parameters, order, sizes, orders);  // g_1<a name="line.437"></a>
<FONT color="green">438</FONT>                    for (int j = 2; j &lt; term.length; ++j) {<a name="line.438"></a>
<FONT color="green">439</FONT>                        // convert the indices as the mapping for the current order<a name="line.439"></a>
<FONT color="green">440</FONT>                        // is different from the mapping with one less order<a name="line.440"></a>
<FONT color="green">441</FONT>                        derivedTermF[j] = convertIndex(term[j], parameters,<a name="line.441"></a>
<FONT color="green">442</FONT>                                                       derivativeCompiler.derivativesIndirection,<a name="line.442"></a>
<FONT color="green">443</FONT>                                                       parameters, order, sizes);<a name="line.443"></a>
<FONT color="green">444</FONT>                    }<a name="line.444"></a>
<FONT color="green">445</FONT>                    Arrays.sort(derivedTermF, 2, derivedTermF.length);<a name="line.445"></a>
<FONT color="green">446</FONT>                    row.add(derivedTermF);<a name="line.446"></a>
<FONT color="green">447</FONT>    <a name="line.447"></a>
<FONT color="green">448</FONT>                    // derive the various g_l<a name="line.448"></a>
<FONT color="green">449</FONT>                    for (int l = 2; l &lt; term.length; ++l) {<a name="line.449"></a>
<FONT color="green">450</FONT>                        int[] derivedTermG = new int[term.length];<a name="line.450"></a>
<FONT color="green">451</FONT>                        derivedTermG[0] = term[0];<a name="line.451"></a>
<FONT color="green">452</FONT>                        derivedTermG[1] = term[1];<a name="line.452"></a>
<FONT color="green">453</FONT>                        for (int j = 2; j &lt; term.length; ++j) {<a name="line.453"></a>
<FONT color="green">454</FONT>                            // convert the indices as the mapping for the current order<a name="line.454"></a>
<FONT color="green">455</FONT>                            // is different from the mapping with one less order<a name="line.455"></a>
<FONT color="green">456</FONT>                            derivedTermG[j] = convertIndex(term[j], parameters,<a name="line.456"></a>
<FONT color="green">457</FONT>                                                           derivativeCompiler.derivativesIndirection,<a name="line.457"></a>
<FONT color="green">458</FONT>                                                           parameters, order, sizes);<a name="line.458"></a>
<FONT color="green">459</FONT>                            if (j == l) {<a name="line.459"></a>
<FONT color="green">460</FONT>                                // derive this term<a name="line.460"></a>
<FONT color="green">461</FONT>                                System.arraycopy(derivativesIndirection[derivedTermG[j]], 0, orders, 0, parameters);<a name="line.461"></a>
<FONT color="green">462</FONT>                                orders[parameters - 1]++;<a name="line.462"></a>
<FONT color="green">463</FONT>                                derivedTermG[j] = getPartialDerivativeIndex(parameters, order, sizes, orders);<a name="line.463"></a>
<FONT color="green">464</FONT>                            }<a name="line.464"></a>
<FONT color="green">465</FONT>                        }<a name="line.465"></a>
<FONT color="green">466</FONT>                        Arrays.sort(derivedTermG, 2, derivedTermG.length);<a name="line.466"></a>
<FONT color="green">467</FONT>                        row.add(derivedTermG);<a name="line.467"></a>
<FONT color="green">468</FONT>                    }<a name="line.468"></a>
<FONT color="green">469</FONT>    <a name="line.469"></a>
<FONT color="green">470</FONT>                }<a name="line.470"></a>
<FONT color="green">471</FONT>    <a name="line.471"></a>
<FONT color="green">472</FONT>                // combine terms with similar derivation orders<a name="line.472"></a>
<FONT color="green">473</FONT>                final List&lt;int[]&gt; combined = new ArrayList&lt;int[]&gt;(row.size());<a name="line.473"></a>
<FONT color="green">474</FONT>                for (int j = 0; j &lt; row.size(); ++j) {<a name="line.474"></a>
<FONT color="green">475</FONT>                    final int[] termJ = row.get(j);<a name="line.475"></a>
<FONT color="green">476</FONT>                    if (termJ[0] &gt; 0) {<a name="line.476"></a>
<FONT color="green">477</FONT>                        for (int k = j + 1; k &lt; row.size(); ++k) {<a name="line.477"></a>
<FONT color="green">478</FONT>                            final int[] termK = row.get(k);<a name="line.478"></a>
<FONT color="green">479</FONT>                            boolean equals = termJ.length == termK.length;<a name="line.479"></a>
<FONT color="green">480</FONT>                            for (int l = 1; equals &amp;&amp; l &lt; termJ.length; ++l) {<a name="line.480"></a>
<FONT color="green">481</FONT>                                equals &amp;= termJ[l] == termK[l];<a name="line.481"></a>
<FONT color="green">482</FONT>                            }<a name="line.482"></a>
<FONT color="green">483</FONT>                            if (equals) {<a name="line.483"></a>
<FONT color="green">484</FONT>                                // combine termJ and termK<a name="line.484"></a>
<FONT color="green">485</FONT>                                termJ[0] += termK[0];<a name="line.485"></a>
<FONT color="green">486</FONT>                                // make sure we will skip termK later on in the outer loop<a name="line.486"></a>
<FONT color="green">487</FONT>                                termK[0] = 0;<a name="line.487"></a>
<FONT color="green">488</FONT>                            }<a name="line.488"></a>
<FONT color="green">489</FONT>                        }<a name="line.489"></a>
<FONT color="green">490</FONT>                        combined.add(termJ);<a name="line.490"></a>
<FONT color="green">491</FONT>                    }<a name="line.491"></a>
<FONT color="green">492</FONT>                }<a name="line.492"></a>
<FONT color="green">493</FONT>    <a name="line.493"></a>
<FONT color="green">494</FONT>                compIndirection[vSize + i] = combined.toArray(new int[combined.size()][]);<a name="line.494"></a>
<FONT color="green">495</FONT>    <a name="line.495"></a>
<FONT color="green">496</FONT>            }<a name="line.496"></a>
<FONT color="green">497</FONT>    <a name="line.497"></a>
<FONT color="green">498</FONT>            return compIndirection;<a name="line.498"></a>
<FONT color="green">499</FONT>    <a name="line.499"></a>
<FONT color="green">500</FONT>        }<a name="line.500"></a>
<FONT color="green">501</FONT>    <a name="line.501"></a>
<FONT color="green">502</FONT>        /** Get the index of a partial derivative in the array.<a name="line.502"></a>
<FONT color="green">503</FONT>         * &lt;p&gt;<a name="line.503"></a>
<FONT color="green">504</FONT>         * If all orders are set to 0, then the 0&lt;sup&gt;th&lt;/sup&gt; order derivative<a name="line.504"></a>
<FONT color="green">505</FONT>         * is returned, which is the value of the function.<a name="line.505"></a>
<FONT color="green">506</FONT>         * &lt;/p&gt;<a name="line.506"></a>
<FONT color="green">507</FONT>         * &lt;p&gt;The indices of derivatives are between 0 and {@link #getSize() getSize()} - 1.<a name="line.507"></a>
<FONT color="green">508</FONT>         * Their specific order is fixed for a given compiler, but otherwise not<a name="line.508"></a>
<FONT color="green">509</FONT>         * publicly specified. There are however some simple cases which have guaranteed<a name="line.509"></a>
<FONT color="green">510</FONT>         * indices:<a name="line.510"></a>
<FONT color="green">511</FONT>         * &lt;/p&gt;<a name="line.511"></a>
<FONT color="green">512</FONT>         * &lt;ul&gt;<a name="line.512"></a>
<FONT color="green">513</FONT>         *   &lt;li&gt;the index of 0&lt;sup&gt;th&lt;/sup&gt; order derivative is always 0&lt;/li&gt;<a name="line.513"></a>
<FONT color="green">514</FONT>         *   &lt;li&gt;if there is only 1 {@link #getFreeParameters() free parameter}, then the<a name="line.514"></a>
<FONT color="green">515</FONT>         *   derivatives are sorted in increasing derivation order (i.e. f at index 0, df/dp<a name="line.515"></a>
<FONT color="green">516</FONT>         *   at index 1, d&lt;sup&gt;2&lt;/sup&gt;f/dp&lt;sup&gt;2&lt;/sup&gt; at index 2 ...<a name="line.516"></a>
<FONT color="green">517</FONT>         *   d&lt;sup&gt;k&lt;/sup&gt;f/dp&lt;sup&gt;k&lt;/sup&gt; at index k),&lt;/li&gt;<a name="line.517"></a>
<FONT color="green">518</FONT>         *   &lt;li&gt;if the {@link #getOrder() derivation order} is 1, then the derivatives<a name="line.518"></a>
<FONT color="green">519</FONT>         *   are sorted in incresing free parameter order (i.e. f at index 0, df/dx&lt;sub&gt;1&lt;/sub&gt;<a name="line.519"></a>
<FONT color="green">520</FONT>         *   at index 1, df/dx&lt;sub&gt;2&lt;/sub&gt; at index 2 ... df/dx&lt;sub&gt;k&lt;/sub&gt; at index k),&lt;/li&gt;<a name="line.520"></a>
<FONT color="green">521</FONT>         *   &lt;li&gt;all other cases are not publicly specified&lt;/li&gt;<a name="line.521"></a>
<FONT color="green">522</FONT>         * &lt;/ul&gt;<a name="line.522"></a>
<FONT color="green">523</FONT>         * &lt;p&gt;<a name="line.523"></a>
<FONT color="green">524</FONT>         * This method is the inverse of method {@link #getPartialDerivativeOrders(int)}<a name="line.524"></a>
<FONT color="green">525</FONT>         * &lt;/p&gt;<a name="line.525"></a>
<FONT color="green">526</FONT>         * @param orders derivation orders with respect to each parameter<a name="line.526"></a>
<FONT color="green">527</FONT>         * @return index of the partial derivative<a name="line.527"></a>
<FONT color="green">528</FONT>         * @exception DimensionMismatchException if the numbers of parameters does not<a name="line.528"></a>
<FONT color="green">529</FONT>         * match the instance<a name="line.529"></a>
<FONT color="green">530</FONT>         * @exception NumberIsTooLargeException if sum of derivation orders is larger<a name="line.530"></a>
<FONT color="green">531</FONT>         * than the instance limits<a name="line.531"></a>
<FONT color="green">532</FONT>         * @see #getPartialDerivativeOrders(int)<a name="line.532"></a>
<FONT color="green">533</FONT>         */<a name="line.533"></a>
<FONT color="green">534</FONT>        public int getPartialDerivativeIndex(final int ... orders)<a name="line.534"></a>
<FONT color="green">535</FONT>                throws DimensionMismatchException, NumberIsTooLargeException {<a name="line.535"></a>
<FONT color="green">536</FONT>    <a name="line.536"></a>
<FONT color="green">537</FONT>            // safety check<a name="line.537"></a>
<FONT color="green">538</FONT>            if (orders.length != getFreeParameters()) {<a name="line.538"></a>
<FONT color="green">539</FONT>                throw new DimensionMismatchException(orders.length, getFreeParameters());<a name="line.539"></a>
<FONT color="green">540</FONT>            }<a name="line.540"></a>
<FONT color="green">541</FONT>    <a name="line.541"></a>
<FONT color="green">542</FONT>            return getPartialDerivativeIndex(parameters, order, sizes, orders);<a name="line.542"></a>
<FONT color="green">543</FONT>    <a name="line.543"></a>
<FONT color="green">544</FONT>        }<a name="line.544"></a>
<FONT color="green">545</FONT>    <a name="line.545"></a>
<FONT color="green">546</FONT>        /** Get the index of a partial derivative in an array.<a name="line.546"></a>
<FONT color="green">547</FONT>         * @param parameters number of free parameters<a name="line.547"></a>
<FONT color="green">548</FONT>         * @param order derivation order<a name="line.548"></a>
<FONT color="green">549</FONT>         * @param sizes sizes array<a name="line.549"></a>
<FONT color="green">550</FONT>         * @param orders derivation orders with respect to each parameter<a name="line.550"></a>
<FONT color="green">551</FONT>         * (the lenght of this array must match the number of parameters)<a name="line.551"></a>
<FONT color="green">552</FONT>         * @return index of the partial derivative<a name="line.552"></a>
<FONT color="green">553</FONT>         * @exception NumberIsTooLargeException if sum of derivation orders is larger<a name="line.553"></a>
<FONT color="green">554</FONT>         * than the instance limits<a name="line.554"></a>
<FONT color="green">555</FONT>         */<a name="line.555"></a>
<FONT color="green">556</FONT>        private static int getPartialDerivativeIndex(final int parameters, final int order,<a name="line.556"></a>
<FONT color="green">557</FONT>                                                     final int[][] sizes, final int ... orders)<a name="line.557"></a>
<FONT color="green">558</FONT>            throws NumberIsTooLargeException {<a name="line.558"></a>
<FONT color="green">559</FONT>    <a name="line.559"></a>
<FONT color="green">560</FONT>            // the value is obtained by diving into the recursive Dan Kalman's structure<a name="line.560"></a>
<FONT color="green">561</FONT>            // this is theorem 2 of his paper, with recursion replaced by iteration<a name="line.561"></a>
<FONT color="green">562</FONT>            int index     = 0;<a name="line.562"></a>
<FONT color="green">563</FONT>            int m         = order;<a name="line.563"></a>
<FONT color="green">564</FONT>            int ordersSum = 0;<a name="line.564"></a>
<FONT color="green">565</FONT>            for (int i = parameters - 1; i &gt;= 0; --i) {<a name="line.565"></a>
<FONT color="green">566</FONT>    <a name="line.566"></a>
<FONT color="green">567</FONT>                // derivative order for current free parameter<a name="line.567"></a>
<FONT color="green">568</FONT>                int derivativeOrder = orders[i];<a name="line.568"></a>
<FONT color="green">569</FONT>    <a name="line.569"></a>
<FONT color="green">570</FONT>                // safety check<a name="line.570"></a>
<FONT color="green">571</FONT>                ordersSum += derivativeOrder;<a name="line.571"></a>
<FONT color="green">572</FONT>                if (ordersSum &gt; order) {<a name="line.572"></a>
<FONT color="green">573</FONT>                    throw new NumberIsTooLargeException(ordersSum, order, true);<a name="line.573"></a>
<FONT color="green">574</FONT>                }<a name="line.574"></a>
<FONT color="green">575</FONT>    <a name="line.575"></a>
<FONT color="green">576</FONT>                while (derivativeOrder-- &gt; 0) {<a name="line.576"></a>
<FONT color="green">577</FONT>                    // as long as we differentiate according to current free parameter,<a name="line.577"></a>
<FONT color="green">578</FONT>                    // we have to skip the value part and dive into the derivative part<a name="line.578"></a>
<FONT color="green">579</FONT>                    // so we add the size of the value part to the base index<a name="line.579"></a>
<FONT color="green">580</FONT>                    index += sizes[i][m--];<a name="line.580"></a>
<FONT color="green">581</FONT>                }<a name="line.581"></a>
<FONT color="green">582</FONT>    <a name="line.582"></a>
<FONT color="green">583</FONT>            }<a name="line.583"></a>
<FONT color="green">584</FONT>    <a name="line.584"></a>
<FONT color="green">585</FONT>            return index;<a name="line.585"></a>
<FONT color="green">586</FONT>    <a name="line.586"></a>
<FONT color="green">587</FONT>        }<a name="line.587"></a>
<FONT color="green">588</FONT>    <a name="line.588"></a>
<FONT color="green">589</FONT>        /** Convert an index from one (parameters, order) structure to another.<a name="line.589"></a>
<FONT color="green">590</FONT>         * @param index index of a partial derivative in source derivative structure<a name="line.590"></a>
<FONT color="green">591</FONT>         * @param srcP number of free parameters in source derivative structure<a name="line.591"></a>
<FONT color="green">592</FONT>         * @param srcDerivativesIndirection derivatives indirection array for the source<a name="line.592"></a>
<FONT color="green">593</FONT>         * derivative structure<a name="line.593"></a>
<FONT color="green">594</FONT>         * @param destP number of free parameters in destination derivative structure<a name="line.594"></a>
<FONT color="green">595</FONT>         * @param destO derivation order in destination derivative structure<a name="line.595"></a>
<FONT color="green">596</FONT>         * @param destSizes sizes array for the destination derivative structure<a name="line.596"></a>
<FONT color="green">597</FONT>         * @return index of the partial derivative with the &lt;em&gt;same&lt;/em&gt; characteristics<a name="line.597"></a>
<FONT color="green">598</FONT>         * in destination derivative structure<a name="line.598"></a>
<FONT color="green">599</FONT>         */<a name="line.599"></a>
<FONT color="green">600</FONT>        private static int convertIndex(final int index,<a name="line.600"></a>
<FONT color="green">601</FONT>                                        final int srcP, final int[][] srcDerivativesIndirection,<a name="line.601"></a>
<FONT color="green">602</FONT>                                        final int destP, final int destO, final int[][] destSizes) {<a name="line.602"></a>
<FONT color="green">603</FONT>            int[] orders = new int[destP];<a name="line.603"></a>
<FONT color="green">604</FONT>            System.arraycopy(srcDerivativesIndirection[index], 0, orders, 0, FastMath.min(srcP, destP));<a name="line.604"></a>
<FONT color="green">605</FONT>            return getPartialDerivativeIndex(destP, destO, destSizes, orders);<a name="line.605"></a>
<FONT color="green">606</FONT>        }<a name="line.606"></a>
<FONT color="green">607</FONT>    <a name="line.607"></a>
<FONT color="green">608</FONT>        /** Get the derivation orders for a specific index in the array.<a name="line.608"></a>
<FONT color="green">609</FONT>         * &lt;p&gt;<a name="line.609"></a>
<FONT color="green">610</FONT>         * This method is the inverse of {@link #getPartialDerivativeIndex(int...)}.<a name="line.610"></a>
<FONT color="green">611</FONT>         * &lt;/p&gt;<a name="line.611"></a>
<FONT color="green">612</FONT>         * @param index of the partial derivative<a name="line.612"></a>
<FONT color="green">613</FONT>         * @return orders derivation orders with respect to each parameter<a name="line.613"></a>
<FONT color="green">614</FONT>         * @see #getPartialDerivativeIndex(int...)<a name="line.614"></a>
<FONT color="green">615</FONT>         */<a name="line.615"></a>
<FONT color="green">616</FONT>        public int[] getPartialDerivativeOrders(final int index) {<a name="line.616"></a>
<FONT color="green">617</FONT>            return derivativesIndirection[index];<a name="line.617"></a>
<FONT color="green">618</FONT>        }<a name="line.618"></a>
<FONT color="green">619</FONT>    <a name="line.619"></a>
<FONT color="green">620</FONT>        /** Get the number of free parameters.<a name="line.620"></a>
<FONT color="green">621</FONT>         * @return number of free parameters<a name="line.621"></a>
<FONT color="green">622</FONT>         */<a name="line.622"></a>
<FONT color="green">623</FONT>        public int getFreeParameters() {<a name="line.623"></a>
<FONT color="green">624</FONT>            return parameters;<a name="line.624"></a>
<FONT color="green">625</FONT>        }<a name="line.625"></a>
<FONT color="green">626</FONT>    <a name="line.626"></a>
<FONT color="green">627</FONT>        /** Get the derivation order.<a name="line.627"></a>
<FONT color="green">628</FONT>         * @return derivation order<a name="line.628"></a>
<FONT color="green">629</FONT>         */<a name="line.629"></a>
<FONT color="green">630</FONT>        public int getOrder() {<a name="line.630"></a>
<FONT color="green">631</FONT>            return order;<a name="line.631"></a>
<FONT color="green">632</FONT>        }<a name="line.632"></a>
<FONT color="green">633</FONT>    <a name="line.633"></a>
<FONT color="green">634</FONT>        /** Get the array size required for holding partial derivatives data.<a name="line.634"></a>
<FONT color="green">635</FONT>         * &lt;p&gt;<a name="line.635"></a>
<FONT color="green">636</FONT>         * This number includes the single 0 order derivative element, which is<a name="line.636"></a>
<FONT color="green">637</FONT>         * guaranteed to be stored in the first element of the array.<a name="line.637"></a>
<FONT color="green">638</FONT>         * &lt;/p&gt;<a name="line.638"></a>
<FONT color="green">639</FONT>         * @return array size required for holding partial derivatives data<a name="line.639"></a>
<FONT color="green">640</FONT>         */<a name="line.640"></a>
<FONT color="green">641</FONT>        public int getSize() {<a name="line.641"></a>
<FONT color="green">642</FONT>            return sizes[parameters][order];<a name="line.642"></a>
<FONT color="green">643</FONT>        }<a name="line.643"></a>
<FONT color="green">644</FONT>    <a name="line.644"></a>
<FONT color="green">645</FONT>        /** Compute linear combination.<a name="line.645"></a>
<FONT color="green">646</FONT>         * The derivative structure built will be a1 * ds1 + a2 * ds2<a name="line.646"></a>
<FONT color="green">647</FONT>         * @param a1 first scale factor<a name="line.647"></a>
<FONT color="green">648</FONT>         * @param c1 first base (unscaled) component<a name="line.648"></a>
<FONT color="green">649</FONT>         * @param offset1 offset of first operand in its array<a name="line.649"></a>
<FONT color="green">650</FONT>         * @param a2 second scale factor<a name="line.650"></a>
<FONT color="green">651</FONT>         * @param c2 second base (unscaled) component<a name="line.651"></a>
<FONT color="green">652</FONT>         * @param offset2 offset of second operand in its array<a name="line.652"></a>
<FONT color="green">653</FONT>         * @param result array where result must be stored (it may be<a name="line.653"></a>
<FONT color="green">654</FONT>         * one of the input arrays)<a name="line.654"></a>
<FONT color="green">655</FONT>         * @param resultOffset offset of the result in its array<a name="line.655"></a>
<FONT color="green">656</FONT>         */<a name="line.656"></a>
<FONT color="green">657</FONT>        public void linearCombination(final double a1, final double[] c1, final int offset1,<a name="line.657"></a>
<FONT color="green">658</FONT>                                      final double a2, final double[] c2, final int offset2,<a name="line.658"></a>
<FONT color="green">659</FONT>                                      final double[] result, final int resultOffset) {<a name="line.659"></a>
<FONT color="green">660</FONT>            for (int i = 0; i &lt; getSize(); ++i) {<a name="line.660"></a>
<FONT color="green">661</FONT>                result[resultOffset + i] =<a name="line.661"></a>
<FONT color="green">662</FONT>                        MathArrays.linearCombination(a1, c1[offset1 + i], a2, c2[offset2 + i]);<a name="line.662"></a>
<FONT color="green">663</FONT>            }<a name="line.663"></a>
<FONT color="green">664</FONT>        }<a name="line.664"></a>
<FONT color="green">665</FONT>    <a name="line.665"></a>
<FONT color="green">666</FONT>        /** Compute linear combination.<a name="line.666"></a>
<FONT color="green">667</FONT>         * The derivative structure built will be a1 * ds1 + a2 * ds2 + a3 * ds3 + a4 * ds4<a name="line.667"></a>
<FONT color="green">668</FONT>         * @param a1 first scale factor<a name="line.668"></a>
<FONT color="green">669</FONT>         * @param c1 first base (unscaled) component<a name="line.669"></a>
<FONT color="green">670</FONT>         * @param offset1 offset of first operand in its array<a name="line.670"></a>
<FONT color="green">671</FONT>         * @param a2 second scale factor<a name="line.671"></a>
<FONT color="green">672</FONT>         * @param c2 second base (unscaled) component<a name="line.672"></a>
<FONT color="green">673</FONT>         * @param offset2 offset of second operand in its array<a name="line.673"></a>
<FONT color="green">674</FONT>         * @param a3 third scale factor<a name="line.674"></a>
<FONT color="green">675</FONT>         * @param c3 third base (unscaled) component<a name="line.675"></a>
<FONT color="green">676</FONT>         * @param offset3 offset of third operand in its array<a name="line.676"></a>
<FONT color="green">677</FONT>         * @param result array where result must be stored (it may be<a name="line.677"></a>
<FONT color="green">678</FONT>         * one of the input arrays)<a name="line.678"></a>
<FONT color="green">679</FONT>         * @param resultOffset offset of the result in its array<a name="line.679"></a>
<FONT color="green">680</FONT>         */<a name="line.680"></a>
<FONT color="green">681</FONT>        public void linearCombination(final double a1, final double[] c1, final int offset1,<a name="line.681"></a>
<FONT color="green">682</FONT>                                      final double a2, final double[] c2, final int offset2,<a name="line.682"></a>
<FONT color="green">683</FONT>                                      final double a3, final double[] c3, final int offset3,<a name="line.683"></a>
<FONT color="green">684</FONT>                                      final double[] result, final int resultOffset) {<a name="line.684"></a>
<FONT color="green">685</FONT>            for (int i = 0; i &lt; getSize(); ++i) {<a name="line.685"></a>
<FONT color="green">686</FONT>                result[resultOffset + i] =<a name="line.686"></a>
<FONT color="green">687</FONT>                        MathArrays.linearCombination(a1, c1[offset1 + i],<a name="line.687"></a>
<FONT color="green">688</FONT>                                                     a2, c2[offset2 + i],<a name="line.688"></a>
<FONT color="green">689</FONT>                                                     a3, c3[offset3 + i]);<a name="line.689"></a>
<FONT color="green">690</FONT>            }<a name="line.690"></a>
<FONT color="green">691</FONT>        }<a name="line.691"></a>
<FONT color="green">692</FONT>    <a name="line.692"></a>
<FONT color="green">693</FONT>        /** Compute linear combination.<a name="line.693"></a>
<FONT color="green">694</FONT>         * The derivative structure built will be a1 * ds1 + a2 * ds2 + a3 * ds3 + a4 * ds4<a name="line.694"></a>
<FONT color="green">695</FONT>         * @param a1 first scale factor<a name="line.695"></a>
<FONT color="green">696</FONT>         * @param c1 first base (unscaled) component<a name="line.696"></a>
<FONT color="green">697</FONT>         * @param offset1 offset of first operand in its array<a name="line.697"></a>
<FONT color="green">698</FONT>         * @param a2 second scale factor<a name="line.698"></a>
<FONT color="green">699</FONT>         * @param c2 second base (unscaled) component<a name="line.699"></a>
<FONT color="green">700</FONT>         * @param offset2 offset of second operand in its array<a name="line.700"></a>
<FONT color="green">701</FONT>         * @param a3 third scale factor<a name="line.701"></a>
<FONT color="green">702</FONT>         * @param c3 third base (unscaled) component<a name="line.702"></a>
<FONT color="green">703</FONT>         * @param offset3 offset of third operand in its array<a name="line.703"></a>
<FONT color="green">704</FONT>         * @param a4 fourth scale factor<a name="line.704"></a>
<FONT color="green">705</FONT>         * @param c4 fourth base (unscaled) component<a name="line.705"></a>
<FONT color="green">706</FONT>         * @param offset4 offset of fourth operand in its array<a name="line.706"></a>
<FONT color="green">707</FONT>         * @param result array where result must be stored (it may be<a name="line.707"></a>
<FONT color="green">708</FONT>         * one of the input arrays)<a name="line.708"></a>
<FONT color="green">709</FONT>         * @param resultOffset offset of the result in its array<a name="line.709"></a>
<FONT color="green">710</FONT>         */<a name="line.710"></a>
<FONT color="green">711</FONT>        public void linearCombination(final double a1, final double[] c1, final int offset1,<a name="line.711"></a>
<FONT color="green">712</FONT>                                      final double a2, final double[] c2, final int offset2,<a name="line.712"></a>
<FONT color="green">713</FONT>                                      final double a3, final double[] c3, final int offset3,<a name="line.713"></a>
<FONT color="green">714</FONT>                                      final double a4, final double[] c4, final int offset4,<a name="line.714"></a>
<FONT color="green">715</FONT>                                      final double[] result, final int resultOffset) {<a name="line.715"></a>
<FONT color="green">716</FONT>            for (int i = 0; i &lt; getSize(); ++i) {<a name="line.716"></a>
<FONT color="green">717</FONT>                result[resultOffset + i] =<a name="line.717"></a>
<FONT color="green">718</FONT>                        MathArrays.linearCombination(a1, c1[offset1 + i],<a name="line.718"></a>
<FONT color="green">719</FONT>                                                     a2, c2[offset2 + i],<a name="line.719"></a>
<FONT color="green">720</FONT>                                                     a3, c3[offset3 + i],<a name="line.720"></a>
<FONT color="green">721</FONT>                                                     a4, c4[offset4 + i]);<a name="line.721"></a>
<FONT color="green">722</FONT>            }<a name="line.722"></a>
<FONT color="green">723</FONT>        }<a name="line.723"></a>
<FONT color="green">724</FONT>    <a name="line.724"></a>
<FONT color="green">725</FONT>        /** Perform addition of two derivative structures.<a name="line.725"></a>
<FONT color="green">726</FONT>         * @param lhs array holding left hand side of addition<a name="line.726"></a>
<FONT color="green">727</FONT>         * @param lhsOffset offset of the left hand side in its array<a name="line.727"></a>
<FONT color="green">728</FONT>         * @param rhs array right hand side of addition<a name="line.728"></a>
<FONT color="green">729</FONT>         * @param rhsOffset offset of the right hand side in its array<a name="line.729"></a>
<FONT color="green">730</FONT>         * @param result array where result must be stored (it may be<a name="line.730"></a>
<FONT color="green">731</FONT>         * one of the input arrays)<a name="line.731"></a>
<FONT color="green">732</FONT>         * @param resultOffset offset of the result in its array<a name="line.732"></a>
<FONT color="green">733</FONT>         */<a name="line.733"></a>
<FONT color="green">734</FONT>        public void add(final double[] lhs, final int lhsOffset,<a name="line.734"></a>
<FONT color="green">735</FONT>                        final double[] rhs, final int rhsOffset,<a name="line.735"></a>
<FONT color="green">736</FONT>                        final double[] result, final int resultOffset) {<a name="line.736"></a>
<FONT color="green">737</FONT>            for (int i = 0; i &lt; getSize(); ++i) {<a name="line.737"></a>
<FONT color="green">738</FONT>                result[resultOffset + i] = lhs[lhsOffset + i] + rhs[rhsOffset + i];<a name="line.738"></a>
<FONT color="green">739</FONT>            }<a name="line.739"></a>
<FONT color="green">740</FONT>        }<a name="line.740"></a>
<FONT color="green">741</FONT>        /** Perform subtraction of two derivative structures.<a name="line.741"></a>
<FONT color="green">742</FONT>         * @param lhs array holding left hand side of subtraction<a name="line.742"></a>
<FONT color="green">743</FONT>         * @param lhsOffset offset of the left hand side in its array<a name="line.743"></a>
<FONT color="green">744</FONT>         * @param rhs array right hand side of subtraction<a name="line.744"></a>
<FONT color="green">745</FONT>         * @param rhsOffset offset of the right hand side in its array<a name="line.745"></a>
<FONT color="green">746</FONT>         * @param result array where result must be stored (it may be<a name="line.746"></a>
<FONT color="green">747</FONT>         * one of the input arrays)<a name="line.747"></a>
<FONT color="green">748</FONT>         * @param resultOffset offset of the result in its array<a name="line.748"></a>
<FONT color="green">749</FONT>         */<a name="line.749"></a>
<FONT color="green">750</FONT>        public void subtract(final double[] lhs, final int lhsOffset,<a name="line.750"></a>
<FONT color="green">751</FONT>                             final double[] rhs, final int rhsOffset,<a name="line.751"></a>
<FONT color="green">752</FONT>                             final double[] result, final int resultOffset) {<a name="line.752"></a>
<FONT color="green">753</FONT>            for (int i = 0; i &lt; getSize(); ++i) {<a name="line.753"></a>
<FONT color="green">754</FONT>                result[resultOffset + i] = lhs[lhsOffset + i] - rhs[rhsOffset + i];<a name="line.754"></a>
<FONT color="green">755</FONT>            }<a name="line.755"></a>
<FONT color="green">756</FONT>        }<a name="line.756"></a>
<FONT color="green">757</FONT>    <a name="line.757"></a>
<FONT color="green">758</FONT>        /** Perform multiplication of two derivative structures.<a name="line.758"></a>
<FONT color="green">759</FONT>         * @param lhs array holding left hand side of multiplication<a name="line.759"></a>
<FONT color="green">760</FONT>         * @param lhsOffset offset of the left hand side in its array<a name="line.760"></a>
<FONT color="green">761</FONT>         * @param rhs array right hand side of multiplication<a name="line.761"></a>
<FONT color="green">762</FONT>         * @param rhsOffset offset of the right hand side in its array<a name="line.762"></a>
<FONT color="green">763</FONT>         * @param result array where result must be stored (for<a name="line.763"></a>
<FONT color="green">764</FONT>         * multiplication the result array &lt;em&gt;cannot&lt;/em&gt; be one of<a name="line.764"></a>
<FONT color="green">765</FONT>         * the input arrays)<a name="line.765"></a>
<FONT color="green">766</FONT>         * @param resultOffset offset of the result in its array<a name="line.766"></a>
<FONT color="green">767</FONT>         */<a name="line.767"></a>
<FONT color="green">768</FONT>        public void multiply(final double[] lhs, final int lhsOffset,<a name="line.768"></a>
<FONT color="green">769</FONT>                             final double[] rhs, final int rhsOffset,<a name="line.769"></a>
<FONT color="green">770</FONT>                             final double[] result, final int resultOffset) {<a name="line.770"></a>
<FONT color="green">771</FONT>            for (int i = 0; i &lt; multIndirection.length; ++i) {<a name="line.771"></a>
<FONT color="green">772</FONT>                final int[][] mappingI = multIndirection[i];<a name="line.772"></a>
<FONT color="green">773</FONT>                double r = 0;<a name="line.773"></a>
<FONT color="green">774</FONT>                for (int j = 0; j &lt; mappingI.length; ++j) {<a name="line.774"></a>
<FONT color="green">775</FONT>                    r += mappingI[j][0] *<a name="line.775"></a>
<FONT color="green">776</FONT>                         lhs[lhsOffset + mappingI[j][1]] *<a name="line.776"></a>
<FONT color="green">777</FONT>                         rhs[rhsOffset + mappingI[j][2]];<a name="line.777"></a>
<FONT color="green">778</FONT>                }<a name="line.778"></a>
<FONT color="green">779</FONT>                result[resultOffset + i] = r;<a name="line.779"></a>
<FONT color="green">780</FONT>            }<a name="line.780"></a>
<FONT color="green">781</FONT>        }<a name="line.781"></a>
<FONT color="green">782</FONT>    <a name="line.782"></a>
<FONT color="green">783</FONT>        /** Perform division of two derivative structures.<a name="line.783"></a>
<FONT color="green">784</FONT>         * @param lhs array holding left hand side of division<a name="line.784"></a>
<FONT color="green">785</FONT>         * @param lhsOffset offset of the left hand side in its array<a name="line.785"></a>
<FONT color="green">786</FONT>         * @param rhs array right hand side of division<a name="line.786"></a>
<FONT color="green">787</FONT>         * @param rhsOffset offset of the right hand side in its array<a name="line.787"></a>
<FONT color="green">788</FONT>         * @param result array where result must be stored (for<a name="line.788"></a>
<FONT color="green">789</FONT>         * division the result array &lt;em&gt;cannot&lt;/em&gt; be one of<a name="line.789"></a>
<FONT color="green">790</FONT>         * the input arrays)<a name="line.790"></a>
<FONT color="green">791</FONT>         * @param resultOffset offset of the result in its array<a name="line.791"></a>
<FONT color="green">792</FONT>         */<a name="line.792"></a>
<FONT color="green">793</FONT>        public void divide(final double[] lhs, final int lhsOffset,<a name="line.793"></a>
<FONT color="green">794</FONT>                           final double[] rhs, final int rhsOffset,<a name="line.794"></a>
<FONT color="green">795</FONT>                           final double[] result, final int resultOffset) {<a name="line.795"></a>
<FONT color="green">796</FONT>            final double[] reciprocal = new double[getSize()];<a name="line.796"></a>
<FONT color="green">797</FONT>            pow(rhs, lhsOffset, -1, reciprocal, 0);<a name="line.797"></a>
<FONT color="green">798</FONT>            multiply(lhs, lhsOffset, reciprocal, 0, result, resultOffset);<a name="line.798"></a>
<FONT color="green">799</FONT>        }<a name="line.799"></a>
<FONT color="green">800</FONT>    <a name="line.800"></a>
<FONT color="green">801</FONT>        /** Perform remainder of two derivative structures.<a name="line.801"></a>
<FONT color="green">802</FONT>         * @param lhs array holding left hand side of remainder<a name="line.802"></a>
<FONT color="green">803</FONT>         * @param lhsOffset offset of the left hand side in its array<a name="line.803"></a>
<FONT color="green">804</FONT>         * @param rhs array right hand side of remainder<a name="line.804"></a>
<FONT color="green">805</FONT>         * @param rhsOffset offset of the right hand side in its array<a name="line.805"></a>
<FONT color="green">806</FONT>         * @param result array where result must be stored (it may be<a name="line.806"></a>
<FONT color="green">807</FONT>         * one of the input arrays)<a name="line.807"></a>
<FONT color="green">808</FONT>         * @param resultOffset offset of the result in its array<a name="line.808"></a>
<FONT color="green">809</FONT>         */<a name="line.809"></a>
<FONT color="green">810</FONT>        public void remainder(final double[] lhs, final int lhsOffset,<a name="line.810"></a>
<FONT color="green">811</FONT>                              final double[] rhs, final int rhsOffset,<a name="line.811"></a>
<FONT color="green">812</FONT>                              final double[] result, final int resultOffset) {<a name="line.812"></a>
<FONT color="green">813</FONT>    <a name="line.813"></a>
<FONT color="green">814</FONT>            // compute k such that lhs % rhs = lhs - k rhs<a name="line.814"></a>
<FONT color="green">815</FONT>            final double rem = lhs[lhsOffset] % rhs[rhsOffset];<a name="line.815"></a>
<FONT color="green">816</FONT>            final double k   = FastMath.rint((lhs[lhsOffset] - rem) / rhs[rhsOffset]);<a name="line.816"></a>
<FONT color="green">817</FONT>    <a name="line.817"></a>
<FONT color="green">818</FONT>            // set up value<a name="line.818"></a>
<FONT color="green">819</FONT>            result[resultOffset] = rem;<a name="line.819"></a>
<FONT color="green">820</FONT>    <a name="line.820"></a>
<FONT color="green">821</FONT>            // set up partial derivatives<a name="line.821"></a>
<FONT color="green">822</FONT>            for (int i = 1; i &lt; getSize(); ++i) {<a name="line.822"></a>
<FONT color="green">823</FONT>                result[resultOffset + i] = lhs[lhsOffset + i] - k * rhs[rhsOffset + i];<a name="line.823"></a>
<FONT color="green">824</FONT>            }<a name="line.824"></a>
<FONT color="green">825</FONT>    <a name="line.825"></a>
<FONT color="green">826</FONT>        }<a name="line.826"></a>
<FONT color="green">827</FONT>    <a name="line.827"></a>
<FONT color="green">828</FONT>        /** Compute power of a derivative structure.<a name="line.828"></a>
<FONT color="green">829</FONT>         * @param operand array holding the operand<a name="line.829"></a>
<FONT color="green">830</FONT>         * @param operandOffset offset of the operand in its array<a name="line.830"></a>
<FONT color="green">831</FONT>         * @param p power to apply<a name="line.831"></a>
<FONT color="green">832</FONT>         * @param result array where result must be stored (for<a name="line.832"></a>
<FONT color="green">833</FONT>         * power the result array &lt;em&gt;cannot&lt;/em&gt; be the input<a name="line.833"></a>
<FONT color="green">834</FONT>         * array)<a name="line.834"></a>
<FONT color="green">835</FONT>         * @param resultOffset offset of the result in its array<a name="line.835"></a>
<FONT color="green">836</FONT>         */<a name="line.836"></a>
<FONT color="green">837</FONT>        public void pow(final double[] operand, final int operandOffset, final double p,<a name="line.837"></a>
<FONT color="green">838</FONT>                        final double[] result, final int resultOffset) {<a name="line.838"></a>
<FONT color="green">839</FONT>    <a name="line.839"></a>
<FONT color="green">840</FONT>            // create the function value and derivatives<a name="line.840"></a>
<FONT color="green">841</FONT>            // [x^p, px^(p-1), p(p-1)x^(p-2), ... ]<a name="line.841"></a>
<FONT color="green">842</FONT>            double[] function = new double[1 + order];<a name="line.842"></a>
<FONT color="green">843</FONT>            double xk = FastMath.pow(operand[operandOffset], p - order);<a name="line.843"></a>
<FONT color="green">844</FONT>            for (int i = order; i &gt; 0; --i) {<a name="line.844"></a>
<FONT color="green">845</FONT>                function[i] = xk;<a name="line.845"></a>
<FONT color="green">846</FONT>                xk *= operand[operandOffset];<a name="line.846"></a>
<FONT color="green">847</FONT>            }<a name="line.847"></a>
<FONT color="green">848</FONT>            function[0] = xk;<a name="line.848"></a>
<FONT color="green">849</FONT>            double coefficient = p;<a name="line.849"></a>
<FONT color="green">850</FONT>            for (int i = 1; i &lt;= order; ++i) {<a name="line.850"></a>
<FONT color="green">851</FONT>                function[i] *= coefficient;<a name="line.851"></a>
<FONT color="green">852</FONT>                coefficient *= p - i;<a name="line.852"></a>
<FONT color="green">853</FONT>            }<a name="line.853"></a>
<FONT color="green">854</FONT>    <a name="line.854"></a>
<FONT color="green">855</FONT>            // apply function composition<a name="line.855"></a>
<FONT color="green">856</FONT>            compose(operand, operandOffset, function, result, resultOffset);<a name="line.856"></a>
<FONT color="green">857</FONT>    <a name="line.857"></a>
<FONT color="green">858</FONT>        }<a name="line.858"></a>
<FONT color="green">859</FONT>    <a name="line.859"></a>
<FONT color="green">860</FONT>        /** Compute integer power of a derivative structure.<a name="line.860"></a>
<FONT color="green">861</FONT>         * @param operand array holding the operand<a name="line.861"></a>
<FONT color="green">862</FONT>         * @param operandOffset offset of the operand in its array<a name="line.862"></a>
<FONT color="green">863</FONT>         * @param n power to apply<a name="line.863"></a>
<FONT color="green">864</FONT>         * @param result array where result must be stored (for<a name="line.864"></a>
<FONT color="green">865</FONT>         * power the result array &lt;em&gt;cannot&lt;/em&gt; be the input<a name="line.865"></a>
<FONT color="green">866</FONT>         * array)<a name="line.866"></a>
<FONT color="green">867</FONT>         * @param resultOffset offset of the result in its array<a name="line.867"></a>
<FONT color="green">868</FONT>         */<a name="line.868"></a>
<FONT color="green">869</FONT>        public void pow(final double[] operand, final int operandOffset, final int n,<a name="line.869"></a>
<FONT color="green">870</FONT>                        final double[] result, final int resultOffset) {<a name="line.870"></a>
<FONT color="green">871</FONT>    <a name="line.871"></a>
<FONT color="green">872</FONT>            if (n == 0) {<a name="line.872"></a>
<FONT color="green">873</FONT>                // special case, x^0 = 1 for all x<a name="line.873"></a>
<FONT color="green">874</FONT>                result[resultOffset] = 1.0;<a name="line.874"></a>
<FONT color="green">875</FONT>                Arrays.fill(result, resultOffset + 1, resultOffset + getSize(), 0);<a name="line.875"></a>
<FONT color="green">876</FONT>                return;<a name="line.876"></a>
<FONT color="green">877</FONT>            }<a name="line.877"></a>
<FONT color="green">878</FONT>    <a name="line.878"></a>
<FONT color="green">879</FONT>            // create the power function value and derivatives<a name="line.879"></a>
<FONT color="green">880</FONT>            // [x^n, nx^(n-1), n(n-1)x^(n-2), ... ]<a name="line.880"></a>
<FONT color="green">881</FONT>            double[] function = new double[1 + order];<a name="line.881"></a>
<FONT color="green">882</FONT>    <a name="line.882"></a>
<FONT color="green">883</FONT>            if (n &gt; 0) {<a name="line.883"></a>
<FONT color="green">884</FONT>                // strictly positive power<a name="line.884"></a>
<FONT color="green">885</FONT>                final int maxOrder = FastMath.min(order, n);<a name="line.885"></a>
<FONT color="green">886</FONT>                double xk = FastMath.pow(operand[operandOffset], n - maxOrder);<a name="line.886"></a>
<FONT color="green">887</FONT>                for (int i = maxOrder; i &gt; 0; --i) {<a name="line.887"></a>
<FONT color="green">888</FONT>                    function[i] = xk;<a name="line.888"></a>
<FONT color="green">889</FONT>                    xk *= operand[operandOffset];<a name="line.889"></a>
<FONT color="green">890</FONT>                }<a name="line.890"></a>
<FONT color="green">891</FONT>                function[0] = xk;<a name="line.891"></a>
<FONT color="green">892</FONT>            } else {<a name="line.892"></a>
<FONT color="green">893</FONT>                // strictly negative power<a name="line.893"></a>
<FONT color="green">894</FONT>                final double inv = 1.0 / operand[operandOffset];<a name="line.894"></a>
<FONT color="green">895</FONT>                double xk = FastMath.pow(inv, -n);<a name="line.895"></a>
<FONT color="green">896</FONT>                for (int i = 0; i &lt;= order; ++i) {<a name="line.896"></a>
<FONT color="green">897</FONT>                    function[i] = xk;<a name="line.897"></a>
<FONT color="green">898</FONT>                    xk *= inv;<a name="line.898"></a>
<FONT color="green">899</FONT>                }<a name="line.899"></a>
<FONT color="green">900</FONT>            }<a name="line.900"></a>
<FONT color="green">901</FONT>    <a name="line.901"></a>
<FONT color="green">902</FONT>            double coefficient = n;<a name="line.902"></a>
<FONT color="green">903</FONT>            for (int i = 1; i &lt;= order; ++i) {<a name="line.903"></a>
<FONT color="green">904</FONT>                function[i] *= coefficient;<a name="line.904"></a>
<FONT color="green">905</FONT>                coefficient *= n - i;<a name="line.905"></a>
<FONT color="green">906</FONT>            }<a name="line.906"></a>
<FONT color="green">907</FONT>    <a name="line.907"></a>
<FONT color="green">908</FONT>            // apply function composition<a name="line.908"></a>
<FONT color="green">909</FONT>            compose(operand, operandOffset, function, result, resultOffset);<a name="line.909"></a>
<FONT color="green">910</FONT>    <a name="line.910"></a>
<FONT color="green">911</FONT>        }<a name="line.911"></a>
<FONT color="green">912</FONT>    <a name="line.912"></a>
<FONT color="green">913</FONT>        /** Compute power of a derivative structure.<a name="line.913"></a>
<FONT color="green">914</FONT>         * @param x array holding the base<a name="line.914"></a>
<FONT color="green">915</FONT>         * @param xOffset offset of the base in its array<a name="line.915"></a>
<FONT color="green">916</FONT>         * @param y array holding the exponent<a name="line.916"></a>
<FONT color="green">917</FONT>         * @param yOffset offset of the exponent in its array<a name="line.917"></a>
<FONT color="green">918</FONT>         * @param result array where result must be stored (for<a name="line.918"></a>
<FONT color="green">919</FONT>         * power the result array &lt;em&gt;cannot&lt;/em&gt; be the input<a name="line.919"></a>
<FONT color="green">920</FONT>         * array)<a name="line.920"></a>
<FONT color="green">921</FONT>         * @param resultOffset offset of the result in its array<a name="line.921"></a>
<FONT color="green">922</FONT>         */<a name="line.922"></a>
<FONT color="green">923</FONT>        public void pow(final double[] x, final int xOffset,<a name="line.923"></a>
<FONT color="green">924</FONT>                        final double[] y, final int yOffset,<a name="line.924"></a>
<FONT color="green">925</FONT>                        final double[] result, final int resultOffset) {<a name="line.925"></a>
<FONT color="green">926</FONT>            final double[] logX = new double[getSize()];<a name="line.926"></a>
<FONT color="green">927</FONT>            log(x, xOffset, logX, 0);<a name="line.927"></a>
<FONT color="green">928</FONT>            final double[] yLogX = new double[getSize()];<a name="line.928"></a>
<FONT color="green">929</FONT>            multiply(logX, 0, y, yOffset, yLogX, 0);<a name="line.929"></a>
<FONT color="green">930</FONT>            exp(yLogX, 0, result, resultOffset);<a name="line.930"></a>
<FONT color="green">931</FONT>        }<a name="line.931"></a>
<FONT color="green">932</FONT>    <a name="line.932"></a>
<FONT color="green">933</FONT>        /** Compute n&lt;sup&gt;th&lt;/sup&gt; root of a derivative structure.<a name="line.933"></a>
<FONT color="green">934</FONT>         * @param operand array holding the operand<a name="line.934"></a>
<FONT color="green">935</FONT>         * @param operandOffset offset of the operand in its array<a name="line.935"></a>
<FONT color="green">936</FONT>         * @param n order of the root<a name="line.936"></a>
<FONT color="green">937</FONT>         * @param result array where result must be stored (for<a name="line.937"></a>
<FONT color="green">938</FONT>         * n&lt;sup&gt;th&lt;/sup&gt; root the result array &lt;em&gt;cannot&lt;/em&gt; be the input<a name="line.938"></a>
<FONT color="green">939</FONT>         * array)<a name="line.939"></a>
<FONT color="green">940</FONT>         * @param resultOffset offset of the result in its array<a name="line.940"></a>
<FONT color="green">941</FONT>         */<a name="line.941"></a>
<FONT color="green">942</FONT>        public void rootN(final double[] operand, final int operandOffset, final int n,<a name="line.942"></a>
<FONT color="green">943</FONT>                          final double[] result, final int resultOffset) {<a name="line.943"></a>
<FONT color="green">944</FONT>    <a name="line.944"></a>
<FONT color="green">945</FONT>            // create the function value and derivatives<a name="line.945"></a>
<FONT color="green">946</FONT>            // [x^(1/n), (1/n)x^((1/n)-1), (1-n)/n^2x^((1/n)-2), ... ]<a name="line.946"></a>
<FONT color="green">947</FONT>            double[] function = new double[1 + order];<a name="line.947"></a>
<FONT color="green">948</FONT>            double xk;<a name="line.948"></a>
<FONT color="green">949</FONT>            if (n == 2) {<a name="line.949"></a>
<FONT color="green">950</FONT>                function[0] = FastMath.sqrt(operand[operandOffset]);<a name="line.950"></a>
<FONT color="green">951</FONT>                xk          = 0.5 / function[0];<a name="line.951"></a>
<FONT color="green">952</FONT>            } else if (n == 3) {<a name="line.952"></a>
<FONT color="green">953</FONT>                function[0] = FastMath.cbrt(operand[operandOffset]);<a name="line.953"></a>
<FONT color="green">954</FONT>                xk          = 1.0 / (3.0 * function[0] * function[0]);<a name="line.954"></a>
<FONT color="green">955</FONT>            } else {<a name="line.955"></a>
<FONT color="green">956</FONT>                function[0] = FastMath.pow(operand[operandOffset], 1.0 / n);<a name="line.956"></a>
<FONT color="green">957</FONT>                xk          = 1.0 / (n * FastMath.pow(function[0], n - 1));<a name="line.957"></a>
<FONT color="green">958</FONT>            }<a name="line.958"></a>
<FONT color="green">959</FONT>            final double nReciprocal = 1.0 / n;<a name="line.959"></a>
<FONT color="green">960</FONT>            final double xReciprocal = 1.0 / operand[operandOffset];<a name="line.960"></a>
<FONT color="green">961</FONT>            for (int i = 1; i &lt;= order; ++i) {<a name="line.961"></a>
<FONT color="green">962</FONT>                function[i] = xk;<a name="line.962"></a>
<FONT color="green">963</FONT>                xk *= xReciprocal * (nReciprocal - i);<a name="line.963"></a>
<FONT color="green">964</FONT>            }<a name="line.964"></a>
<FONT color="green">965</FONT>    <a name="line.965"></a>
<FONT color="green">966</FONT>            // apply function composition<a name="line.966"></a>
<FONT color="green">967</FONT>            compose(operand, operandOffset, function, result, resultOffset);<a name="line.967"></a>
<FONT color="green">968</FONT>    <a name="line.968"></a>
<FONT color="green">969</FONT>        }<a name="line.969"></a>
<FONT color="green">970</FONT>    <a name="line.970"></a>
<FONT color="green">971</FONT>        /** Compute exponential of a derivative structure.<a name="line.971"></a>
<FONT color="green">972</FONT>         * @param operand array holding the operand<a name="line.972"></a>
<FONT color="green">973</FONT>         * @param operandOffset offset of the operand in its array<a name="line.973"></a>
<FONT color="green">974</FONT>         * @param result array where result must be stored (for<a name="line.974"></a>
<FONT color="green">975</FONT>         * exponential the result array &lt;em&gt;cannot&lt;/em&gt; be the input<a name="line.975"></a>
<FONT color="green">976</FONT>         * array)<a name="line.976"></a>
<FONT color="green">977</FONT>         * @param resultOffset offset of the result in its array<a name="line.977"></a>
<FONT color="green">978</FONT>         */<a name="line.978"></a>
<FONT color="green">979</FONT>        public void exp(final double[] operand, final int operandOffset,<a name="line.979"></a>
<FONT color="green">980</FONT>                        final double[] result, final int resultOffset) {<a name="line.980"></a>
<FONT color="green">981</FONT>    <a name="line.981"></a>
<FONT color="green">982</FONT>            // create the function value and derivatives<a name="line.982"></a>
<FONT color="green">983</FONT>            double[] function = new double[1 + order];<a name="line.983"></a>
<FONT color="green">984</FONT>            Arrays.fill(function, FastMath.exp(operand[operandOffset]));<a name="line.984"></a>
<FONT color="green">985</FONT>    <a name="line.985"></a>
<FONT color="green">986</FONT>            // apply function composition<a name="line.986"></a>
<FONT color="green">987</FONT>            compose(operand, operandOffset, function, result, resultOffset);<a name="line.987"></a>
<FONT color="green">988</FONT>    <a name="line.988"></a>
<FONT color="green">989</FONT>        }<a name="line.989"></a>
<FONT color="green">990</FONT>    <a name="line.990"></a>
<FONT color="green">991</FONT>        /** Compute exp(x) - 1 of a derivative structure.<a name="line.991"></a>
<FONT color="green">992</FONT>         * @param operand array holding the operand<a name="line.992"></a>
<FONT color="green">993</FONT>         * @param operandOffset offset of the operand in its array<a name="line.993"></a>
<FONT color="green">994</FONT>         * @param result array where result must be stored (for<a name="line.994"></a>
<FONT color="green">995</FONT>         * exponential the result array &lt;em&gt;cannot&lt;/em&gt; be the input<a name="line.995"></a>
<FONT color="green">996</FONT>         * array)<a name="line.996"></a>
<FONT color="green">997</FONT>         * @param resultOffset offset of the result in its array<a name="line.997"></a>
<FONT color="green">998</FONT>         */<a name="line.998"></a>
<FONT color="green">999</FONT>        public void expm1(final double[] operand, final int operandOffset,<a name="line.999"></a>
<FONT color="green">1000</FONT>                          final double[] result, final int resultOffset) {<a name="line.1000"></a>
<FONT color="green">1001</FONT>    <a name="line.1001"></a>
<FONT color="green">1002</FONT>            // create the function value and derivatives<a name="line.1002"></a>
<FONT color="green">1003</FONT>            double[] function = new double[1 + order];<a name="line.1003"></a>
<FONT color="green">1004</FONT>            function[0] = FastMath.expm1(operand[operandOffset]);<a name="line.1004"></a>
<FONT color="green">1005</FONT>            Arrays.fill(function, 1, 1 + order, FastMath.exp(operand[operandOffset]));<a name="line.1005"></a>
<FONT color="green">1006</FONT>    <a name="line.1006"></a>
<FONT color="green">1007</FONT>            // apply function composition<a name="line.1007"></a>
<FONT color="green">1008</FONT>            compose(operand, operandOffset, function, result, resultOffset);<a name="line.1008"></a>
<FONT color="green">1009</FONT>    <a name="line.1009"></a>
<FONT color="green">1010</FONT>        }<a name="line.1010"></a>
<FONT color="green">1011</FONT>    <a name="line.1011"></a>
<FONT color="green">1012</FONT>        /** Compute natural logarithm of a derivative structure.<a name="line.1012"></a>
<FONT color="green">1013</FONT>         * @param operand array holding the operand<a name="line.1013"></a>
<FONT color="green">1014</FONT>         * @param operandOffset offset of the operand in its array<a name="line.1014"></a>
<FONT color="green">1015</FONT>         * @param result array where result must be stored (for<a name="line.1015"></a>
<FONT color="green">1016</FONT>         * logarithm the result array &lt;em&gt;cannot&lt;/em&gt; be the input<a name="line.1016"></a>
<FONT color="green">1017</FONT>         * array)<a name="line.1017"></a>
<FONT color="green">1018</FONT>         * @param resultOffset offset of the result in its array<a name="line.1018"></a>
<FONT color="green">1019</FONT>         */<a name="line.1019"></a>
<FONT color="green">1020</FONT>        public void log(final double[] operand, final int operandOffset,<a name="line.1020"></a>
<FONT color="green">1021</FONT>                        final double[] result, final int resultOffset) {<a name="line.1021"></a>
<FONT color="green">1022</FONT>    <a name="line.1022"></a>
<FONT color="green">1023</FONT>            // create the function value and derivatives<a name="line.1023"></a>
<FONT color="green">1024</FONT>            double[] function = new double[1 + order];<a name="line.1024"></a>
<FONT color="green">1025</FONT>            function[0] = FastMath.log(operand[operandOffset]);<a name="line.1025"></a>
<FONT color="green">1026</FONT>            if (order &gt; 0) {<a name="line.1026"></a>
<FONT color="green">1027</FONT>                double inv = 1.0 / operand[operandOffset];<a name="line.1027"></a>
<FONT color="green">1028</FONT>                double xk  = inv;<a name="line.1028"></a>
<FONT color="green">1029</FONT>                for (int i = 1; i &lt;= order; ++i) {<a name="line.1029"></a>
<FONT color="green">1030</FONT>                    function[i] = xk;<a name="line.1030"></a>
<FONT color="green">1031</FONT>                    xk *= -i * inv;<a name="line.1031"></a>
<FONT color="green">1032</FONT>                }<a name="line.1032"></a>
<FONT color="green">1033</FONT>            }<a name="line.1033"></a>
<FONT color="green">1034</FONT>    <a name="line.1034"></a>
<FONT color="green">1035</FONT>            // apply function composition<a name="line.1035"></a>
<FONT color="green">1036</FONT>            compose(operand, operandOffset, function, result, resultOffset);<a name="line.1036"></a>
<FONT color="green">1037</FONT>    <a name="line.1037"></a>
<FONT color="green">1038</FONT>        }<a name="line.1038"></a>
<FONT color="green">1039</FONT>    <a name="line.1039"></a>
<FONT color="green">1040</FONT>        /** Computes shifted logarithm of a derivative structure.<a name="line.1040"></a>
<FONT color="green">1041</FONT>         * @param operand array holding the operand<a name="line.1041"></a>
<FONT color="green">1042</FONT>         * @param operandOffset offset of the operand in its array<a name="line.1042"></a>
<FONT color="green">1043</FONT>         * @param result array where result must be stored (for<a name="line.1043"></a>
<FONT color="green">1044</FONT>         * shifted logarithm the result array &lt;em&gt;cannot&lt;/em&gt; be the input array)<a name="line.1044"></a>
<FONT color="green">1045</FONT>         * @param resultOffset offset of the result in its array<a name="line.1045"></a>
<FONT color="green">1046</FONT>         */<a name="line.1046"></a>
<FONT color="green">1047</FONT>        public void log1p(final double[] operand, final int operandOffset,<a name="line.1047"></a>
<FONT color="green">1048</FONT>                          final double[] result, final int resultOffset) {<a name="line.1048"></a>
<FONT color="green">1049</FONT>    <a name="line.1049"></a>
<FONT color="green">1050</FONT>            // create the function value and derivatives<a name="line.1050"></a>
<FONT color="green">1051</FONT>            double[] function = new double[1 + order];<a name="line.1051"></a>
<FONT color="green">1052</FONT>            function[0] = FastMath.log1p(operand[operandOffset]);<a name="line.1052"></a>
<FONT color="green">1053</FONT>            if (order &gt; 0) {<a name="line.1053"></a>
<FONT color="green">1054</FONT>                double inv = 1.0 / (1.0 + operand[operandOffset]);<a name="line.1054"></a>
<FONT color="green">1055</FONT>                double xk  = inv;<a name="line.1055"></a>
<FONT color="green">1056</FONT>                for (int i = 1; i &lt;= order; ++i) {<a name="line.1056"></a>
<FONT color="green">1057</FONT>                    function[i] = xk;<a name="line.1057"></a>
<FONT color="green">1058</FONT>                    xk *= -i * inv;<a name="line.1058"></a>
<FONT color="green">1059</FONT>                }<a name="line.1059"></a>
<FONT color="green">1060</FONT>            }<a name="line.1060"></a>
<FONT color="green">1061</FONT>    <a name="line.1061"></a>
<FONT color="green">1062</FONT>            // apply function composition<a name="line.1062"></a>
<FONT color="green">1063</FONT>            compose(operand, operandOffset, function, result, resultOffset);<a name="line.1063"></a>
<FONT color="green">1064</FONT>    <a name="line.1064"></a>
<FONT color="green">1065</FONT>        }<a name="line.1065"></a>
<FONT color="green">1066</FONT>    <a name="line.1066"></a>
<FONT color="green">1067</FONT>        /** Computes base 10 logarithm of a derivative structure.<a name="line.1067"></a>
<FONT color="green">1068</FONT>         * @param operand array holding the operand<a name="line.1068"></a>
<FONT color="green">1069</FONT>         * @param operandOffset offset of the operand in its array<a name="line.1069"></a>
<FONT color="green">1070</FONT>         * @param result array where result must be stored (for<a name="line.1070"></a>
<FONT color="green">1071</FONT>         * base 10 logarithm the result array &lt;em&gt;cannot&lt;/em&gt; be the input array)<a name="line.1071"></a>
<FONT color="green">1072</FONT>         * @param resultOffset offset of the result in its array<a name="line.1072"></a>
<FONT color="green">1073</FONT>         */<a name="line.1073"></a>
<FONT color="green">1074</FONT>        public void log10(final double[] operand, final int operandOffset,<a name="line.1074"></a>
<FONT color="green">1075</FONT>                          final double[] result, final int resultOffset) {<a name="line.1075"></a>
<FONT color="green">1076</FONT>    <a name="line.1076"></a>
<FONT color="green">1077</FONT>            // create the function value and derivatives<a name="line.1077"></a>
<FONT color="green">1078</FONT>            double[] function = new double[1 + order];<a name="line.1078"></a>
<FONT color="green">1079</FONT>            function[0] = FastMath.log10(operand[operandOffset]);<a name="line.1079"></a>
<FONT color="green">1080</FONT>            if (order &gt; 0) {<a name="line.1080"></a>
<FONT color="green">1081</FONT>                double inv = 1.0 / operand[operandOffset];<a name="line.1081"></a>
<FONT color="green">1082</FONT>                double xk  = inv / FastMath.log(10.0);<a name="line.1082"></a>
<FONT color="green">1083</FONT>                for (int i = 1; i &lt;= order; ++i) {<a name="line.1083"></a>
<FONT color="green">1084</FONT>                    function[i] = xk;<a name="line.1084"></a>
<FONT color="green">1085</FONT>                    xk *= -i * inv;<a name="line.1085"></a>
<FONT color="green">1086</FONT>                }<a name="line.1086"></a>
<FONT color="green">1087</FONT>            }<a name="line.1087"></a>
<FONT color="green">1088</FONT>    <a name="line.1088"></a>
<FONT color="green">1089</FONT>            // apply function composition<a name="line.1089"></a>
<FONT color="green">1090</FONT>            compose(operand, operandOffset, function, result, resultOffset);<a name="line.1090"></a>
<FONT color="green">1091</FONT>    <a name="line.1091"></a>
<FONT color="green">1092</FONT>        }<a name="line.1092"></a>
<FONT color="green">1093</FONT>    <a name="line.1093"></a>
<FONT color="green">1094</FONT>        /** Compute cosine of a derivative structure.<a name="line.1094"></a>
<FONT color="green">1095</FONT>         * @param operand array holding the operand<a name="line.1095"></a>
<FONT color="green">1096</FONT>         * @param operandOffset offset of the operand in its array<a name="line.1096"></a>
<FONT color="green">1097</FONT>         * @param result array where result must be stored (for<a name="line.1097"></a>
<FONT color="green">1098</FONT>         * cosine the result array &lt;em&gt;cannot&lt;/em&gt; be the input<a name="line.1098"></a>
<FONT color="green">1099</FONT>         * array)<a name="line.1099"></a>
<FONT color="green">1100</FONT>         * @param resultOffset offset of the result in its array<a name="line.1100"></a>
<FONT color="green">1101</FONT>         */<a name="line.1101"></a>
<FONT color="green">1102</FONT>        public void cos(final double[] operand, final int operandOffset,<a name="line.1102"></a>
<FONT color="green">1103</FONT>                        final double[] result, final int resultOffset) {<a name="line.1103"></a>
<FONT color="green">1104</FONT>    <a name="line.1104"></a>
<FONT color="green">1105</FONT>            // create the function value and derivatives<a name="line.1105"></a>
<FONT color="green">1106</FONT>            double[] function = new double[1 + order];<a name="line.1106"></a>
<FONT color="green">1107</FONT>            function[0] = FastMath.cos(operand[operandOffset]);<a name="line.1107"></a>
<FONT color="green">1108</FONT>            if (order &gt; 0) {<a name="line.1108"></a>
<FONT color="green">1109</FONT>                function[1] = -FastMath.sin(operand[operandOffset]);<a name="line.1109"></a>
<FONT color="green">1110</FONT>                for (int i = 2; i &lt;= order; ++i) {<a name="line.1110"></a>
<FONT color="green">1111</FONT>                    function[i] = -function[i - 2];<a name="line.1111"></a>
<FONT color="green">1112</FONT>                }<a name="line.1112"></a>
<FONT color="green">1113</FONT>            }<a name="line.1113"></a>
<FONT color="green">1114</FONT>    <a name="line.1114"></a>
<FONT color="green">1115</FONT>            // apply function composition<a name="line.1115"></a>
<FONT color="green">1116</FONT>            compose(operand, operandOffset, function, result, resultOffset);<a name="line.1116"></a>
<FONT color="green">1117</FONT>    <a name="line.1117"></a>
<FONT color="green">1118</FONT>        }<a name="line.1118"></a>
<FONT color="green">1119</FONT>    <a name="line.1119"></a>
<FONT color="green">1120</FONT>        /** Compute sine of a derivative structure.<a name="line.1120"></a>
<FONT color="green">1121</FONT>         * @param operand array holding the operand<a name="line.1121"></a>
<FONT color="green">1122</FONT>         * @param operandOffset offset of the operand in its array<a name="line.1122"></a>
<FONT color="green">1123</FONT>         * @param result array where result must be stored (for<a name="line.1123"></a>
<FONT color="green">1124</FONT>         * sine the result array &lt;em&gt;cannot&lt;/em&gt; be the input<a name="line.1124"></a>
<FONT color="green">1125</FONT>         * array)<a name="line.1125"></a>
<FONT color="green">1126</FONT>         * @param resultOffset offset of the result in its array<a name="line.1126"></a>
<FONT color="green">1127</FONT>         */<a name="line.1127"></a>
<FONT color="green">1128</FONT>        public void sin(final double[] operand, final int operandOffset,<a name="line.1128"></a>
<FONT color="green">1129</FONT>                        final double[] result, final int resultOffset) {<a name="line.1129"></a>
<FONT color="green">1130</FONT>    <a name="line.1130"></a>
<FONT color="green">1131</FONT>            // create the function value and derivatives<a name="line.1131"></a>
<FONT color="green">1132</FONT>            double[] function = new double[1 + order];<a name="line.1132"></a>
<FONT color="green">1133</FONT>            function[0] = FastMath.sin(operand[operandOffset]);<a name="line.1133"></a>
<FONT color="green">1134</FONT>            if (order &gt; 0) {<a name="line.1134"></a>
<FONT color="green">1135</FONT>                function[1] = FastMath.cos(operand[operandOffset]);<a name="line.1135"></a>
<FONT color="green">1136</FONT>                for (int i = 2; i &lt;= order; ++i) {<a name="line.1136"></a>
<FONT color="green">1137</FONT>                    function[i] = -function[i - 2];<a name="line.1137"></a>
<FONT color="green">1138</FONT>                }<a name="line.1138"></a>
<FONT color="green">1139</FONT>            }<a name="line.1139"></a>
<FONT color="green">1140</FONT>    <a name="line.1140"></a>
<FONT color="green">1141</FONT>            // apply function composition<a name="line.1141"></a>
<FONT color="green">1142</FONT>            compose(operand, operandOffset, function, result, resultOffset);<a name="line.1142"></a>
<FONT color="green">1143</FONT>    <a name="line.1143"></a>
<FONT color="green">1144</FONT>        }<a name="line.1144"></a>
<FONT color="green">1145</FONT>    <a name="line.1145"></a>
<FONT color="green">1146</FONT>        /** Compute tangent of a derivative structure.<a name="line.1146"></a>
<FONT color="green">1147</FONT>         * @param operand array holding the operand<a name="line.1147"></a>
<FONT color="green">1148</FONT>         * @param operandOffset offset of the operand in its array<a name="line.1148"></a>
<FONT color="green">1149</FONT>         * @param result array where result must be stored (for<a name="line.1149"></a>
<FONT color="green">1150</FONT>         * tangent the result array &lt;em&gt;cannot&lt;/em&gt; be the input<a name="line.1150"></a>
<FONT color="green">1151</FONT>         * array)<a name="line.1151"></a>
<FONT color="green">1152</FONT>         * @param resultOffset offset of the result in its array<a name="line.1152"></a>
<FONT color="green">1153</FONT>         */<a name="line.1153"></a>
<FONT color="green">1154</FONT>        public void tan(final double[] operand, final int operandOffset,<a name="line.1154"></a>
<FONT color="green">1155</FONT>                        final double[] result, final int resultOffset) {<a name="line.1155"></a>
<FONT color="green">1156</FONT>    <a name="line.1156"></a>
<FONT color="green">1157</FONT>            // create the function value and derivatives<a name="line.1157"></a>
<FONT color="green">1158</FONT>            final double[] function = new double[1 + order];<a name="line.1158"></a>
<FONT color="green">1159</FONT>            final double t = FastMath.tan(operand[operandOffset]);<a name="line.1159"></a>
<FONT color="green">1160</FONT>            function[0] = t;<a name="line.1160"></a>
<FONT color="green">1161</FONT>    <a name="line.1161"></a>
<FONT color="green">1162</FONT>            if (order &gt; 0) {<a name="line.1162"></a>
<FONT color="green">1163</FONT>    <a name="line.1163"></a>
<FONT color="green">1164</FONT>                // the nth order derivative of tan has the form:<a name="line.1164"></a>
<FONT color="green">1165</FONT>                // dn(tan(x)/dxn = P_n(tan(x))<a name="line.1165"></a>
<FONT color="green">1166</FONT>                // where P_n(t) is a degree n+1 polynomial with same parity as n+1<a name="line.1166"></a>
<FONT color="green">1167</FONT>                // P_0(t) = t, P_1(t) = 1 + t^2, P_2(t) = 2 t (1 + t^2) ...<a name="line.1167"></a>
<FONT color="green">1168</FONT>                // the general recurrence relation for P_n is:<a name="line.1168"></a>
<FONT color="green">1169</FONT>                // P_n(x) = (1+t^2) P_(n-1)'(t)<a name="line.1169"></a>
<FONT color="green">1170</FONT>                // as per polynomial parity, we can store coefficients of both P_(n-1) and P_n in the same array<a name="line.1170"></a>
<FONT color="green">1171</FONT>                final double[] p = new double[order + 2];<a name="line.1171"></a>
<FONT color="green">1172</FONT>                p[1] = 1;<a name="line.1172"></a>
<FONT color="green">1173</FONT>                final double t2 = t * t;<a name="line.1173"></a>
<FONT color="green">1174</FONT>                for (int n = 1; n &lt;= order; ++n) {<a name="line.1174"></a>
<FONT color="green">1175</FONT>    <a name="line.1175"></a>
<FONT color="green">1176</FONT>                    // update and evaluate polynomial P_n(t)<a name="line.1176"></a>
<FONT color="green">1177</FONT>                    double v = 0;<a name="line.1177"></a>
<FONT color="green">1178</FONT>                    p[n + 1] = n * p[n];<a name="line.1178"></a>
<FONT color="green">1179</FONT>                    for (int k = n + 1; k &gt;= 0; k -= 2) {<a name="line.1179"></a>
<FONT color="green">1180</FONT>                        v = v * t2 + p[k];<a name="line.1180"></a>
<FONT color="green">1181</FONT>                        if (k &gt; 2) {<a name="line.1181"></a>
<FONT color="green">1182</FONT>                            p[k - 2] = (k - 1) * p[k - 1] + (k - 3) * p[k - 3];<a name="line.1182"></a>
<FONT color="green">1183</FONT>                        } else if (k == 2) {<a name="line.1183"></a>
<FONT color="green">1184</FONT>                            p[0] = p[1];<a name="line.1184"></a>
<FONT color="green">1185</FONT>                        }<a name="line.1185"></a>
<FONT color="green">1186</FONT>                    }<a name="line.1186"></a>
<FONT color="green">1187</FONT>                    if ((n &amp; 0x1) == 0) {<a name="line.1187"></a>
<FONT color="green">1188</FONT>                        v *= t;<a name="line.1188"></a>
<FONT color="green">1189</FONT>                    }<a name="line.1189"></a>
<FONT color="green">1190</FONT>    <a name="line.1190"></a>
<FONT color="green">1191</FONT>                    function[n] = v;<a name="line.1191"></a>
<FONT color="green">1192</FONT>    <a name="line.1192"></a>
<FONT color="green">1193</FONT>                }<a name="line.1193"></a>
<FONT color="green">1194</FONT>            }<a name="line.1194"></a>
<FONT color="green">1195</FONT>    <a name="line.1195"></a>
<FONT color="green">1196</FONT>            // apply function composition<a name="line.1196"></a>
<FONT color="green">1197</FONT>            compose(operand, operandOffset, function, result, resultOffset);<a name="line.1197"></a>
<FONT color="green">1198</FONT>    <a name="line.1198"></a>
<FONT color="green">1199</FONT>        }<a name="line.1199"></a>
<FONT color="green">1200</FONT>    <a name="line.1200"></a>
<FONT color="green">1201</FONT>        /** Compute arc cosine of a derivative structure.<a name="line.1201"></a>
<FONT color="green">1202</FONT>         * @param operand array holding the operand<a name="line.1202"></a>
<FONT color="green">1203</FONT>         * @param operandOffset offset of the operand in its array<a name="line.1203"></a>
<FONT color="green">1204</FONT>         * @param result array where result must be stored (for<a name="line.1204"></a>
<FONT color="green">1205</FONT>         * arc cosine the result array &lt;em&gt;cannot&lt;/em&gt; be the input<a name="line.1205"></a>
<FONT color="green">1206</FONT>         * array)<a name="line.1206"></a>
<FONT color="green">1207</FONT>         * @param resultOffset offset of the result in its array<a name="line.1207"></a>
<FONT color="green">1208</FONT>         */<a name="line.1208"></a>
<FONT color="green">1209</FONT>        public void acos(final double[] operand, final int operandOffset,<a name="line.1209"></a>
<FONT color="green">1210</FONT>                        final double[] result, final int resultOffset) {<a name="line.1210"></a>
<FONT color="green">1211</FONT>    <a name="line.1211"></a>
<FONT color="green">1212</FONT>            // create the function value and derivatives<a name="line.1212"></a>
<FONT color="green">1213</FONT>            double[] function = new double[1 + order];<a name="line.1213"></a>
<FONT color="green">1214</FONT>            final double x = operand[operandOffset];<a name="line.1214"></a>
<FONT color="green">1215</FONT>            function[0] = FastMath.acos(x);<a name="line.1215"></a>
<FONT color="green">1216</FONT>            if (order &gt; 0) {<a name="line.1216"></a>
<FONT color="green">1217</FONT>                // the nth order derivative of acos has the form:<a name="line.1217"></a>
<FONT color="green">1218</FONT>                // dn(acos(x)/dxn = P_n(x) / [1 - x^2]^((2n-1)/2)<a name="line.1218"></a>
<FONT color="green">1219</FONT>                // where P_n(x) is a degree n-1 polynomial with same parity as n-1<a name="line.1219"></a>
<FONT color="green">1220</FONT>                // P_1(x) = -1, P_2(x) = -x, P_3(x) = -2x^2 - 1 ...<a name="line.1220"></a>
<FONT color="green">1221</FONT>                // the general recurrence relation for P_n is:<a name="line.1221"></a>
<FONT color="green">1222</FONT>                // P_n(x) = (1-x^2) P_(n-1)'(x) + (2n-3) x P_(n-1)(x)<a name="line.1222"></a>
<FONT color="green">1223</FONT>                // as per polynomial parity, we can store coefficients of both P_(n-1) and P_n in the same array<a name="line.1223"></a>
<FONT color="green">1224</FONT>                final double[] p = new double[order];<a name="line.1224"></a>
<FONT color="green">1225</FONT>                p[0] = -1;<a name="line.1225"></a>
<FONT color="green">1226</FONT>                final double x2    = x * x;<a name="line.1226"></a>
<FONT color="green">1227</FONT>                final double f     = 1.0 / (1 - x2);<a name="line.1227"></a>
<FONT color="green">1228</FONT>                double coeff = FastMath.sqrt(f);<a name="line.1228"></a>
<FONT color="green">1229</FONT>                function[1] = coeff * p[0];<a name="line.1229"></a>
<FONT color="green">1230</FONT>                for (int n = 2; n &lt;= order; ++n) {<a name="line.1230"></a>
<FONT color="green">1231</FONT>    <a name="line.1231"></a>
<FONT color="green">1232</FONT>                    // update and evaluate polynomial P_n(x)<a name="line.1232"></a>
<FONT color="green">1233</FONT>                    double v = 0;<a name="line.1233"></a>
<FONT color="green">1234</FONT>                    p[n - 1] = (n - 1) * p[n - 2];<a name="line.1234"></a>
<FONT color="green">1235</FONT>                    for (int k = n - 1; k &gt;= 0; k -= 2) {<a name="line.1235"></a>
<FONT color="green">1236</FONT>                        v = v * x2 + p[k];<a name="line.1236"></a>
<FONT color="green">1237</FONT>                        if (k &gt; 2) {<a name="line.1237"></a>
<FONT color="green">1238</FONT>                            p[k - 2] = (k - 1) * p[k - 1] + (2 * n - k) * p[k - 3];<a name="line.1238"></a>
<FONT color="green">1239</FONT>                        } else if (k == 2) {<a name="line.1239"></a>
<FONT color="green">1240</FONT>                            p[0] = p[1];<a name="line.1240"></a>
<FONT color="green">1241</FONT>                        }<a name="line.1241"></a>
<FONT color="green">1242</FONT>                    }<a name="line.1242"></a>
<FONT color="green">1243</FONT>                    if ((n &amp; 0x1) == 0) {<a name="line.1243"></a>
<FONT color="green">1244</FONT>                        v *= x;<a name="line.1244"></a>
<FONT color="green">1245</FONT>                    }<a name="line.1245"></a>
<FONT color="green">1246</FONT>    <a name="line.1246"></a>
<FONT color="green">1247</FONT>                    coeff *= f;<a name="line.1247"></a>
<FONT color="green">1248</FONT>                    function[n] = coeff * v;<a name="line.1248"></a>
<FONT color="green">1249</FONT>    <a name="line.1249"></a>
<FONT color="green">1250</FONT>                }<a name="line.1250"></a>
<FONT color="green">1251</FONT>            }<a name="line.1251"></a>
<FONT color="green">1252</FONT>    <a name="line.1252"></a>
<FONT color="green">1253</FONT>            // apply function composition<a name="line.1253"></a>
<FONT color="green">1254</FONT>            compose(operand, operandOffset, function, result, resultOffset);<a name="line.1254"></a>
<FONT color="green">1255</FONT>    <a name="line.1255"></a>
<FONT color="green">1256</FONT>        }<a name="line.1256"></a>
<FONT color="green">1257</FONT>    <a name="line.1257"></a>
<FONT color="green">1258</FONT>        /** Compute arc sine of a derivative structure.<a name="line.1258"></a>
<FONT color="green">1259</FONT>         * @param operand array holding the operand<a name="line.1259"></a>
<FONT color="green">1260</FONT>         * @param operandOffset offset of the operand in its array<a name="line.1260"></a>
<FONT color="green">1261</FONT>         * @param result array where result must be stored (for<a name="line.1261"></a>
<FONT color="green">1262</FONT>         * arc sine the result array &lt;em&gt;cannot&lt;/em&gt; be the input<a name="line.1262"></a>
<FONT color="green">1263</FONT>         * array)<a name="line.1263"></a>
<FONT color="green">1264</FONT>         * @param resultOffset offset of the result in its array<a name="line.1264"></a>
<FONT color="green">1265</FONT>         */<a name="line.1265"></a>
<FONT color="green">1266</FONT>        public void asin(final double[] operand, final int operandOffset,<a name="line.1266"></a>
<FONT color="green">1267</FONT>                        final double[] result, final int resultOffset) {<a name="line.1267"></a>
<FONT color="green">1268</FONT>    <a name="line.1268"></a>
<FONT color="green">1269</FONT>            // create the function value and derivatives<a name="line.1269"></a>
<FONT color="green">1270</FONT>            double[] function = new double[1 + order];<a name="line.1270"></a>
<FONT color="green">1271</FONT>            final double x = operand[operandOffset];<a name="line.1271"></a>
<FONT color="green">1272</FONT>            function[0] = FastMath.asin(x);<a name="line.1272"></a>
<FONT color="green">1273</FONT>            if (order &gt; 0) {<a name="line.1273"></a>
<FONT color="green">1274</FONT>                // the nth order derivative of asin has the form:<a name="line.1274"></a>
<FONT color="green">1275</FONT>                // dn(asin(x)/dxn = P_n(x) / [1 - x^2]^((2n-1)/2)<a name="line.1275"></a>
<FONT color="green">1276</FONT>                // where P_n(x) is a degree n-1 polynomial with same parity as n-1<a name="line.1276"></a>
<FONT color="green">1277</FONT>                // P_1(x) = 1, P_2(x) = x, P_3(x) = 2x^2 + 1 ...<a name="line.1277"></a>
<FONT color="green">1278</FONT>                // the general recurrence relation for P_n is:<a name="line.1278"></a>
<FONT color="green">1279</FONT>                // P_n(x) = (1-x^2) P_(n-1)'(x) + (2n-3) x P_(n-1)(x)<a name="line.1279"></a>
<FONT color="green">1280</FONT>                // as per polynomial parity, we can store coefficients of both P_(n-1) and P_n in the same array<a name="line.1280"></a>
<FONT color="green">1281</FONT>                final double[] p = new double[order];<a name="line.1281"></a>
<FONT color="green">1282</FONT>                p[0] = 1;<a name="line.1282"></a>
<FONT color="green">1283</FONT>                final double x2    = x * x;<a name="line.1283"></a>
<FONT color="green">1284</FONT>                final double f     = 1.0 / (1 - x2);<a name="line.1284"></a>
<FONT color="green">1285</FONT>                double coeff = FastMath.sqrt(f);<a name="line.1285"></a>
<FONT color="green">1286</FONT>                function[1] = coeff * p[0];<a name="line.1286"></a>
<FONT color="green">1287</FONT>                for (int n = 2; n &lt;= order; ++n) {<a name="line.1287"></a>
<FONT color="green">1288</FONT>    <a name="line.1288"></a>
<FONT color="green">1289</FONT>                    // update and evaluate polynomial P_n(x)<a name="line.1289"></a>
<FONT color="green">1290</FONT>                    double v = 0;<a name="line.1290"></a>
<FONT color="green">1291</FONT>                    p[n - 1] = (n - 1) * p[n - 2];<a name="line.1291"></a>
<FONT color="green">1292</FONT>                    for (int k = n - 1; k &gt;= 0; k -= 2) {<a name="line.1292"></a>
<FONT color="green">1293</FONT>                        v = v * x2 + p[k];<a name="line.1293"></a>
<FONT color="green">1294</FONT>                        if (k &gt; 2) {<a name="line.1294"></a>
<FONT color="green">1295</FONT>                            p[k - 2] = (k - 1) * p[k - 1] + (2 * n - k) * p[k - 3];<a name="line.1295"></a>
<FONT color="green">1296</FONT>                        } else if (k == 2) {<a name="line.1296"></a>
<FONT color="green">1297</FONT>                            p[0] = p[1];<a name="line.1297"></a>
<FONT color="green">1298</FONT>                        }<a name="line.1298"></a>
<FONT color="green">1299</FONT>                    }<a name="line.1299"></a>
<FONT color="green">1300</FONT>                    if ((n &amp; 0x1) == 0) {<a name="line.1300"></a>
<FONT color="green">1301</FONT>                        v *= x;<a name="line.1301"></a>
<FONT color="green">1302</FONT>                    }<a name="line.1302"></a>
<FONT color="green">1303</FONT>    <a name="line.1303"></a>
<FONT color="green">1304</FONT>                    coeff *= f;<a name="line.1304"></a>
<FONT color="green">1305</FONT>                    function[n] = coeff * v;<a name="line.1305"></a>
<FONT color="green">1306</FONT>    <a name="line.1306"></a>
<FONT color="green">1307</FONT>                }<a name="line.1307"></a>
<FONT color="green">1308</FONT>            }<a name="line.1308"></a>
<FONT color="green">1309</FONT>    <a name="line.1309"></a>
<FONT color="green">1310</FONT>            // apply function composition<a name="line.1310"></a>
<FONT color="green">1311</FONT>            compose(operand, operandOffset, function, result, resultOffset);<a name="line.1311"></a>
<FONT color="green">1312</FONT>    <a name="line.1312"></a>
<FONT color="green">1313</FONT>        }<a name="line.1313"></a>
<FONT color="green">1314</FONT>    <a name="line.1314"></a>
<FONT color="green">1315</FONT>        /** Compute arc tangent of a derivative structure.<a name="line.1315"></a>
<FONT color="green">1316</FONT>         * @param operand array holding the operand<a name="line.1316"></a>
<FONT color="green">1317</FONT>         * @param operandOffset offset of the operand in its array<a name="line.1317"></a>
<FONT color="green">1318</FONT>         * @param result array where result must be stored (for<a name="line.1318"></a>
<FONT color="green">1319</FONT>         * arc tangent the result array &lt;em&gt;cannot&lt;/em&gt; be the input<a name="line.1319"></a>
<FONT color="green">1320</FONT>         * array)<a name="line.1320"></a>
<FONT color="green">1321</FONT>         * @param resultOffset offset of the result in its array<a name="line.1321"></a>
<FONT color="green">1322</FONT>         */<a name="line.1322"></a>
<FONT color="green">1323</FONT>        public void atan(final double[] operand, final int operandOffset,<a name="line.1323"></a>
<FONT color="green">1324</FONT>                         final double[] result, final int resultOffset) {<a name="line.1324"></a>
<FONT color="green">1325</FONT>    <a name="line.1325"></a>
<FONT color="green">1326</FONT>            // create the function value and derivatives<a name="line.1326"></a>
<FONT color="green">1327</FONT>            double[] function = new double[1 + order];<a name="line.1327"></a>
<FONT color="green">1328</FONT>            final double x = operand[operandOffset];<a name="line.1328"></a>
<FONT color="green">1329</FONT>            function[0] = FastMath.atan(x);<a name="line.1329"></a>
<FONT color="green">1330</FONT>            if (order &gt; 0) {<a name="line.1330"></a>
<FONT color="green">1331</FONT>                // the nth order derivative of atan has the form:<a name="line.1331"></a>
<FONT color="green">1332</FONT>                // dn(atan(x)/dxn = Q_n(x) / (1 + x^2)^n<a name="line.1332"></a>
<FONT color="green">1333</FONT>                // where Q_n(x) is a degree n-1 polynomial with same parity as n-1<a name="line.1333"></a>
<FONT color="green">1334</FONT>                // Q_1(x) = 1, Q_2(x) = -2x, Q_3(x) = 6x^2 - 2 ...<a name="line.1334"></a>
<FONT color="green">1335</FONT>                // the general recurrence relation for Q_n is:<a name="line.1335"></a>
<FONT color="green">1336</FONT>                // Q_n(x) = (1+x^2) Q_(n-1)'(x) - 2(n-1) x Q_(n-1)(x)<a name="line.1336"></a>
<FONT color="green">1337</FONT>                // as per polynomial parity, we can store coefficients of both Q_(n-1) and Q_n in the same array<a name="line.1337"></a>
<FONT color="green">1338</FONT>                final double[] q = new double[order];<a name="line.1338"></a>
<FONT color="green">1339</FONT>                q[0] = 1;<a name="line.1339"></a>
<FONT color="green">1340</FONT>                final double x2    = x * x;<a name="line.1340"></a>
<FONT color="green">1341</FONT>                final double f     = 1.0 / (1 + x2);<a name="line.1341"></a>
<FONT color="green">1342</FONT>                double coeff = f;<a name="line.1342"></a>
<FONT color="green">1343</FONT>                function[1] = coeff * q[0];<a name="line.1343"></a>
<FONT color="green">1344</FONT>                for (int n = 2; n &lt;= order; ++n) {<a name="line.1344"></a>
<FONT color="green">1345</FONT>    <a name="line.1345"></a>
<FONT color="green">1346</FONT>                    // update and evaluate polynomial Q_n(x)<a name="line.1346"></a>
<FONT color="green">1347</FONT>                    double v = 0;<a name="line.1347"></a>
<FONT color="green">1348</FONT>                    q[n - 1] = -n * q[n - 2];<a name="line.1348"></a>
<FONT color="green">1349</FONT>                    for (int k = n - 1; k &gt;= 0; k -= 2) {<a name="line.1349"></a>
<FONT color="green">1350</FONT>                        v = v * x2 + q[k];<a name="line.1350"></a>
<FONT color="green">1351</FONT>                        if (k &gt; 2) {<a name="line.1351"></a>
<FONT color="green">1352</FONT>                            q[k - 2] = (k - 1) * q[k - 1] + (k - 1 - 2 * n) * q[k - 3];<a name="line.1352"></a>
<FONT color="green">1353</FONT>                        } else if (k == 2) {<a name="line.1353"></a>
<FONT color="green">1354</FONT>                            q[0] = q[1];<a name="line.1354"></a>
<FONT color="green">1355</FONT>                        }<a name="line.1355"></a>
<FONT color="green">1356</FONT>                    }<a name="line.1356"></a>
<FONT color="green">1357</FONT>                    if ((n &amp; 0x1) == 0) {<a name="line.1357"></a>
<FONT color="green">1358</FONT>                        v *= x;<a name="line.1358"></a>
<FONT color="green">1359</FONT>                    }<a name="line.1359"></a>
<FONT color="green">1360</FONT>    <a name="line.1360"></a>
<FONT color="green">1361</FONT>                    coeff *= f;<a name="line.1361"></a>
<FONT color="green">1362</FONT>                    function[n] = coeff * v;<a name="line.1362"></a>
<FONT color="green">1363</FONT>    <a name="line.1363"></a>
<FONT color="green">1364</FONT>                }<a name="line.1364"></a>
<FONT color="green">1365</FONT>            }<a name="line.1365"></a>
<FONT color="green">1366</FONT>    <a name="line.1366"></a>
<FONT color="green">1367</FONT>            // apply function composition<a name="line.1367"></a>
<FONT color="green">1368</FONT>            compose(operand, operandOffset, function, result, resultOffset);<a name="line.1368"></a>
<FONT color="green">1369</FONT>    <a name="line.1369"></a>
<FONT color="green">1370</FONT>        }<a name="line.1370"></a>
<FONT color="green">1371</FONT>    <a name="line.1371"></a>
<FONT color="green">1372</FONT>        /** Compute two arguments arc tangent of a derivative structure.<a name="line.1372"></a>
<FONT color="green">1373</FONT>         * @param y array holding the first operand<a name="line.1373"></a>
<FONT color="green">1374</FONT>         * @param yOffset offset of the first operand in its array<a name="line.1374"></a>
<FONT color="green">1375</FONT>         * @param x array holding the second operand<a name="line.1375"></a>
<FONT color="green">1376</FONT>         * @param xOffset offset of the second operand in its array<a name="line.1376"></a>
<FONT color="green">1377</FONT>         * @param result array where result must be stored (for<a name="line.1377"></a>
<FONT color="green">1378</FONT>         * two arguments arc tangent the result array &lt;em&gt;cannot&lt;/em&gt;<a name="line.1378"></a>
<FONT color="green">1379</FONT>         * be the input array)<a name="line.1379"></a>
<FONT color="green">1380</FONT>         * @param resultOffset offset of the result in its array<a name="line.1380"></a>
<FONT color="green">1381</FONT>         */<a name="line.1381"></a>
<FONT color="green">1382</FONT>        public void atan2(final double[] y, final int yOffset,<a name="line.1382"></a>
<FONT color="green">1383</FONT>                          final double[] x, final int xOffset,<a name="line.1383"></a>
<FONT color="green">1384</FONT>                          final double[] result, final int resultOffset) {<a name="line.1384"></a>
<FONT color="green">1385</FONT>    <a name="line.1385"></a>
<FONT color="green">1386</FONT>            // compute r = sqrt(x^2+y^2)<a name="line.1386"></a>
<FONT color="green">1387</FONT>            double[] tmp1 = new double[getSize()];<a name="line.1387"></a>
<FONT color="green">1388</FONT>            multiply(x, xOffset, x, xOffset, tmp1, 0);      // x^2<a name="line.1388"></a>
<FONT color="green">1389</FONT>            double[] tmp2 = new double[getSize()];<a name="line.1389"></a>
<FONT color="green">1390</FONT>            multiply(y, yOffset, y, yOffset, tmp2, 0);      // y^2<a name="line.1390"></a>
<FONT color="green">1391</FONT>            add(tmp1, 0, tmp2, 0, tmp2, 0);                 // x^2 + y^2<a name="line.1391"></a>
<FONT color="green">1392</FONT>            rootN(tmp2, 0, 2, tmp1, 0);                     // r = sqrt(x^2 + y^2)<a name="line.1392"></a>
<FONT color="green">1393</FONT>    <a name="line.1393"></a>
<FONT color="green">1394</FONT>            if (x[xOffset] &gt;= 0) {<a name="line.1394"></a>
<FONT color="green">1395</FONT>    <a name="line.1395"></a>
<FONT color="green">1396</FONT>                // compute atan2(y, x) = 2 atan(y / (r + x))<a name="line.1396"></a>
<FONT color="green">1397</FONT>                add(tmp1, 0, x, xOffset, tmp2, 0);          // r + x<a name="line.1397"></a>
<FONT color="green">1398</FONT>                divide(y, yOffset, tmp2, 0, tmp1, 0);       // y /(r + x)<a name="line.1398"></a>
<FONT color="green">1399</FONT>                atan(tmp1, 0, tmp2, 0);                     // atan(y / (r + x))<a name="line.1399"></a>
<FONT color="green">1400</FONT>                for (int i = 0; i &lt; tmp2.length; ++i) {<a name="line.1400"></a>
<FONT color="green">1401</FONT>                    result[resultOffset + i] = 2 * tmp2[i]; // 2 * atan(y / (r + x))<a name="line.1401"></a>
<FONT color="green">1402</FONT>                }<a name="line.1402"></a>
<FONT color="green">1403</FONT>    <a name="line.1403"></a>
<FONT color="green">1404</FONT>            } else {<a name="line.1404"></a>
<FONT color="green">1405</FONT>    <a name="line.1405"></a>
<FONT color="green">1406</FONT>                // compute atan2(y, x) = +/- pi - 2 atan(y / (r - x))<a name="line.1406"></a>
<FONT color="green">1407</FONT>                subtract(tmp1, 0, x, xOffset, tmp2, 0);     // r - x<a name="line.1407"></a>
<FONT color="green">1408</FONT>                divide(y, yOffset, tmp2, 0, tmp1, 0);       // y /(r - x)<a name="line.1408"></a>
<FONT color="green">1409</FONT>                atan(tmp1, 0, tmp2, 0);                     // atan(y / (r - x))<a name="line.1409"></a>
<FONT color="green">1410</FONT>                result[resultOffset] =<a name="line.1410"></a>
<FONT color="green">1411</FONT>                        ((tmp2[0] &lt;= 0) ? -FastMath.PI : FastMath.PI) - 2 * tmp2[0]; // +/-pi - 2 * atan(y / (r - x))<a name="line.1411"></a>
<FONT color="green">1412</FONT>                for (int i = 1; i &lt; tmp2.length; ++i) {<a name="line.1412"></a>
<FONT color="green">1413</FONT>                    result[resultOffset + i] = -2 * tmp2[i]; // +/-pi - 2 * atan(y / (r - x))<a name="line.1413"></a>
<FONT color="green">1414</FONT>                }<a name="line.1414"></a>
<FONT color="green">1415</FONT>    <a name="line.1415"></a>
<FONT color="green">1416</FONT>            }<a name="line.1416"></a>
<FONT color="green">1417</FONT>    <a name="line.1417"></a>
<FONT color="green">1418</FONT>        }<a name="line.1418"></a>
<FONT color="green">1419</FONT>    <a name="line.1419"></a>
<FONT color="green">1420</FONT>        /** Compute hyperbolic cosine of a derivative structure.<a name="line.1420"></a>
<FONT color="green">1421</FONT>         * @param operand array holding the operand<a name="line.1421"></a>
<FONT color="green">1422</FONT>         * @param operandOffset offset of the operand in its array<a name="line.1422"></a>
<FONT color="green">1423</FONT>         * @param result array where result must be stored (for<a name="line.1423"></a>
<FONT color="green">1424</FONT>         * hyperbolic cosine the result array &lt;em&gt;cannot&lt;/em&gt; be the input<a name="line.1424"></a>
<FONT color="green">1425</FONT>         * array)<a name="line.1425"></a>
<FONT color="green">1426</FONT>         * @param resultOffset offset of the result in its array<a name="line.1426"></a>
<FONT color="green">1427</FONT>         */<a name="line.1427"></a>
<FONT color="green">1428</FONT>        public void cosh(final double[] operand, final int operandOffset,<a name="line.1428"></a>
<FONT color="green">1429</FONT>                         final double[] result, final int resultOffset) {<a name="line.1429"></a>
<FONT color="green">1430</FONT>    <a name="line.1430"></a>
<FONT color="green">1431</FONT>            // create the function value and derivatives<a name="line.1431"></a>
<FONT color="green">1432</FONT>            double[] function = new double[1 + order];<a name="line.1432"></a>
<FONT color="green">1433</FONT>            function[0] = FastMath.cosh(operand[operandOffset]);<a name="line.1433"></a>
<FONT color="green">1434</FONT>            if (order &gt; 0) {<a name="line.1434"></a>
<FONT color="green">1435</FONT>                function[1] = FastMath.sinh(operand[operandOffset]);<a name="line.1435"></a>
<FONT color="green">1436</FONT>                for (int i = 2; i &lt;= order; ++i) {<a name="line.1436"></a>
<FONT color="green">1437</FONT>                    function[i] = function[i - 2];<a name="line.1437"></a>
<FONT color="green">1438</FONT>                }<a name="line.1438"></a>
<FONT color="green">1439</FONT>            }<a name="line.1439"></a>
<FONT color="green">1440</FONT>    <a name="line.1440"></a>
<FONT color="green">1441</FONT>            // apply function composition<a name="line.1441"></a>
<FONT color="green">1442</FONT>            compose(operand, operandOffset, function, result, resultOffset);<a name="line.1442"></a>
<FONT color="green">1443</FONT>    <a name="line.1443"></a>
<FONT color="green">1444</FONT>        }<a name="line.1444"></a>
<FONT color="green">1445</FONT>    <a name="line.1445"></a>
<FONT color="green">1446</FONT>        /** Compute hyperbolic sine of a derivative structure.<a name="line.1446"></a>
<FONT color="green">1447</FONT>         * @param operand array holding the operand<a name="line.1447"></a>
<FONT color="green">1448</FONT>         * @param operandOffset offset of the operand in its array<a name="line.1448"></a>
<FONT color="green">1449</FONT>         * @param result array where result must be stored (for<a name="line.1449"></a>
<FONT color="green">1450</FONT>         * hyperbolic sine the result array &lt;em&gt;cannot&lt;/em&gt; be the input<a name="line.1450"></a>
<FONT color="green">1451</FONT>         * array)<a name="line.1451"></a>
<FONT color="green">1452</FONT>         * @param resultOffset offset of the result in its array<a name="line.1452"></a>
<FONT color="green">1453</FONT>         */<a name="line.1453"></a>
<FONT color="green">1454</FONT>        public void sinh(final double[] operand, final int operandOffset,<a name="line.1454"></a>
<FONT color="green">1455</FONT>                         final double[] result, final int resultOffset) {<a name="line.1455"></a>
<FONT color="green">1456</FONT>    <a name="line.1456"></a>
<FONT color="green">1457</FONT>            // create the function value and derivatives<a name="line.1457"></a>
<FONT color="green">1458</FONT>            double[] function = new double[1 + order];<a name="line.1458"></a>
<FONT color="green">1459</FONT>            function[0] = FastMath.sinh(operand[operandOffset]);<a name="line.1459"></a>
<FONT color="green">1460</FONT>            if (order &gt; 0) {<a name="line.1460"></a>
<FONT color="green">1461</FONT>                function[1] = FastMath.cosh(operand[operandOffset]);<a name="line.1461"></a>
<FONT color="green">1462</FONT>                for (int i = 2; i &lt;= order; ++i) {<a name="line.1462"></a>
<FONT color="green">1463</FONT>                    function[i] = function[i - 2];<a name="line.1463"></a>
<FONT color="green">1464</FONT>                }<a name="line.1464"></a>
<FONT color="green">1465</FONT>            }<a name="line.1465"></a>
<FONT color="green">1466</FONT>    <a name="line.1466"></a>
<FONT color="green">1467</FONT>            // apply function composition<a name="line.1467"></a>
<FONT color="green">1468</FONT>            compose(operand, operandOffset, function, result, resultOffset);<a name="line.1468"></a>
<FONT color="green">1469</FONT>    <a name="line.1469"></a>
<FONT color="green">1470</FONT>        }<a name="line.1470"></a>
<FONT color="green">1471</FONT>    <a name="line.1471"></a>
<FONT color="green">1472</FONT>        /** Compute hyperbolic tangent of a derivative structure.<a name="line.1472"></a>
<FONT color="green">1473</FONT>         * @param operand array holding the operand<a name="line.1473"></a>
<FONT color="green">1474</FONT>         * @param operandOffset offset of the operand in its array<a name="line.1474"></a>
<FONT color="green">1475</FONT>         * @param result array where result must be stored (for<a name="line.1475"></a>
<FONT color="green">1476</FONT>         * hyperbolic tangent the result array &lt;em&gt;cannot&lt;/em&gt; be the input<a name="line.1476"></a>
<FONT color="green">1477</FONT>         * array)<a name="line.1477"></a>
<FONT color="green">1478</FONT>         * @param resultOffset offset of the result in its array<a name="line.1478"></a>
<FONT color="green">1479</FONT>         */<a name="line.1479"></a>
<FONT color="green">1480</FONT>        public void tanh(final double[] operand, final int operandOffset,<a name="line.1480"></a>
<FONT color="green">1481</FONT>                         final double[] result, final int resultOffset) {<a name="line.1481"></a>
<FONT color="green">1482</FONT>    <a name="line.1482"></a>
<FONT color="green">1483</FONT>            // create the function value and derivatives<a name="line.1483"></a>
<FONT color="green">1484</FONT>            final double[] function = new double[1 + order];<a name="line.1484"></a>
<FONT color="green">1485</FONT>            final double t = FastMath.tanh(operand[operandOffset]);<a name="line.1485"></a>
<FONT color="green">1486</FONT>            function[0] = t;<a name="line.1486"></a>
<FONT color="green">1487</FONT>    <a name="line.1487"></a>
<FONT color="green">1488</FONT>            if (order &gt; 0) {<a name="line.1488"></a>
<FONT color="green">1489</FONT>    <a name="line.1489"></a>
<FONT color="green">1490</FONT>                // the nth order derivative of tanh has the form:<a name="line.1490"></a>
<FONT color="green">1491</FONT>                // dn(tanh(x)/dxn = P_n(tanh(x))<a name="line.1491"></a>
<FONT color="green">1492</FONT>                // where P_n(t) is a degree n+1 polynomial with same parity as n+1<a name="line.1492"></a>
<FONT color="green">1493</FONT>                // P_0(t) = t, P_1(t) = 1 - t^2, P_2(t) = -2 t (1 - t^2) ...<a name="line.1493"></a>
<FONT color="green">1494</FONT>                // the general recurrence relation for P_n is:<a name="line.1494"></a>
<FONT color="green">1495</FONT>                // P_n(x) = (1-t^2) P_(n-1)'(t)<a name="line.1495"></a>
<FONT color="green">1496</FONT>                // as per polynomial parity, we can store coefficients of both P_(n-1) and P_n in the same array<a name="line.1496"></a>
<FONT color="green">1497</FONT>                final double[] p = new double[order + 2];<a name="line.1497"></a>
<FONT color="green">1498</FONT>                p[1] = 1;<a name="line.1498"></a>
<FONT color="green">1499</FONT>                final double t2 = t * t;<a name="line.1499"></a>
<FONT color="green">1500</FONT>                for (int n = 1; n &lt;= order; ++n) {<a name="line.1500"></a>
<FONT color="green">1501</FONT>    <a name="line.1501"></a>
<FONT color="green">1502</FONT>                    // update and evaluate polynomial P_n(t)<a name="line.1502"></a>
<FONT color="green">1503</FONT>                    double v = 0;<a name="line.1503"></a>
<FONT color="green">1504</FONT>                    p[n + 1] = -n * p[n];<a name="line.1504"></a>
<FONT color="green">1505</FONT>                    for (int k = n + 1; k &gt;= 0; k -= 2) {<a name="line.1505"></a>
<FONT color="green">1506</FONT>                        v = v * t2 + p[k];<a name="line.1506"></a>
<FONT color="green">1507</FONT>                        if (k &gt; 2) {<a name="line.1507"></a>
<FONT color="green">1508</FONT>                            p[k - 2] = (k - 1) * p[k - 1] - (k - 3) * p[k - 3];<a name="line.1508"></a>
<FONT color="green">1509</FONT>                        } else if (k == 2) {<a name="line.1509"></a>
<FONT color="green">1510</FONT>                            p[0] = p[1];<a name="line.1510"></a>
<FONT color="green">1511</FONT>                        }<a name="line.1511"></a>
<FONT color="green">1512</FONT>                    }<a name="line.1512"></a>
<FONT color="green">1513</FONT>                    if ((n &amp; 0x1) == 0) {<a name="line.1513"></a>
<FONT color="green">1514</FONT>                        v *= t;<a name="line.1514"></a>
<FONT color="green">1515</FONT>                    }<a name="line.1515"></a>
<FONT color="green">1516</FONT>    <a name="line.1516"></a>
<FONT color="green">1517</FONT>                    function[n] = v;<a name="line.1517"></a>
<FONT color="green">1518</FONT>    <a name="line.1518"></a>
<FONT color="green">1519</FONT>                }<a name="line.1519"></a>
<FONT color="green">1520</FONT>            }<a name="line.1520"></a>
<FONT color="green">1521</FONT>    <a name="line.1521"></a>
<FONT color="green">1522</FONT>            // apply function composition<a name="line.1522"></a>
<FONT color="green">1523</FONT>            compose(operand, operandOffset, function, result, resultOffset);<a name="line.1523"></a>
<FONT color="green">1524</FONT>    <a name="line.1524"></a>
<FONT color="green">1525</FONT>        }<a name="line.1525"></a>
<FONT color="green">1526</FONT>    <a name="line.1526"></a>
<FONT color="green">1527</FONT>        /** Compute inverse hyperbolic cosine of a derivative structure.<a name="line.1527"></a>
<FONT color="green">1528</FONT>         * @param operand array holding the operand<a name="line.1528"></a>
<FONT color="green">1529</FONT>         * @param operandOffset offset of the operand in its array<a name="line.1529"></a>
<FONT color="green">1530</FONT>         * @param result array where result must be stored (for<a name="line.1530"></a>
<FONT color="green">1531</FONT>         * inverse hyperbolic cosine the result array &lt;em&gt;cannot&lt;/em&gt; be the input<a name="line.1531"></a>
<FONT color="green">1532</FONT>         * array)<a name="line.1532"></a>
<FONT color="green">1533</FONT>         * @param resultOffset offset of the result in its array<a name="line.1533"></a>
<FONT color="green">1534</FONT>         */<a name="line.1534"></a>
<FONT color="green">1535</FONT>        public void acosh(final double[] operand, final int operandOffset,<a name="line.1535"></a>
<FONT color="green">1536</FONT>                         final double[] result, final int resultOffset) {<a name="line.1536"></a>
<FONT color="green">1537</FONT>    <a name="line.1537"></a>
<FONT color="green">1538</FONT>            // create the function value and derivatives<a name="line.1538"></a>
<FONT color="green">1539</FONT>            double[] function = new double[1 + order];<a name="line.1539"></a>
<FONT color="green">1540</FONT>            final double x = operand[operandOffset];<a name="line.1540"></a>
<FONT color="green">1541</FONT>            function[0] = FastMath.acosh(x);<a name="line.1541"></a>
<FONT color="green">1542</FONT>            if (order &gt; 0) {<a name="line.1542"></a>
<FONT color="green">1543</FONT>                // the nth order derivative of acosh has the form:<a name="line.1543"></a>
<FONT color="green">1544</FONT>                // dn(acosh(x)/dxn = P_n(x) / [x^2 - 1]^((2n-1)/2)<a name="line.1544"></a>
<FONT color="green">1545</FONT>                // where P_n(x) is a degree n-1 polynomial with same parity as n-1<a name="line.1545"></a>
<FONT color="green">1546</FONT>                // P_1(x) = 1, P_2(x) = -x, P_3(x) = 2x^2 + 1 ...<a name="line.1546"></a>
<FONT color="green">1547</FONT>                // the general recurrence relation for P_n is:<a name="line.1547"></a>
<FONT color="green">1548</FONT>                // P_n(x) = (x^2-1) P_(n-1)'(x) - (2n-3) x P_(n-1)(x)<a name="line.1548"></a>
<FONT color="green">1549</FONT>                // as per polynomial parity, we can store coefficients of both P_(n-1) and P_n in the same array<a name="line.1549"></a>
<FONT color="green">1550</FONT>                final double[] p = new double[order];<a name="line.1550"></a>
<FONT color="green">1551</FONT>                p[0] = 1;<a name="line.1551"></a>
<FONT color="green">1552</FONT>                final double x2  = x * x;<a name="line.1552"></a>
<FONT color="green">1553</FONT>                final double f   = 1.0 / (x2 - 1);<a name="line.1553"></a>
<FONT color="green">1554</FONT>                double coeff = FastMath.sqrt(f);<a name="line.1554"></a>
<FONT color="green">1555</FONT>                function[1] = coeff * p[0];<a name="line.1555"></a>
<FONT color="green">1556</FONT>                for (int n = 2; n &lt;= order; ++n) {<a name="line.1556"></a>
<FONT color="green">1557</FONT>    <a name="line.1557"></a>
<FONT color="green">1558</FONT>                    // update and evaluate polynomial P_n(x)<a name="line.1558"></a>
<FONT color="green">1559</FONT>                    double v = 0;<a name="line.1559"></a>
<FONT color="green">1560</FONT>                    p[n - 1] = (1 - n) * p[n - 2];<a name="line.1560"></a>
<FONT color="green">1561</FONT>                    for (int k = n - 1; k &gt;= 0; k -= 2) {<a name="line.1561"></a>
<FONT color="green">1562</FONT>                        v = v * x2 + p[k];<a name="line.1562"></a>
<FONT color="green">1563</FONT>                        if (k &gt; 2) {<a name="line.1563"></a>
<FONT color="green">1564</FONT>                            p[k - 2] = (1 - k) * p[k - 1] + (k - 2 * n) * p[k - 3];<a name="line.1564"></a>
<FONT color="green">1565</FONT>                        } else if (k == 2) {<a name="line.1565"></a>
<FONT color="green">1566</FONT>                            p[0] = -p[1];<a name="line.1566"></a>
<FONT color="green">1567</FONT>                        }<a name="line.1567"></a>
<FONT color="green">1568</FONT>                    }<a name="line.1568"></a>
<FONT color="green">1569</FONT>                    if ((n &amp; 0x1) == 0) {<a name="line.1569"></a>
<FONT color="green">1570</FONT>                        v *= x;<a name="line.1570"></a>
<FONT color="green">1571</FONT>                    }<a name="line.1571"></a>
<FONT color="green">1572</FONT>    <a name="line.1572"></a>
<FONT color="green">1573</FONT>                    coeff *= f;<a name="line.1573"></a>
<FONT color="green">1574</FONT>                    function[n] = coeff * v;<a name="line.1574"></a>
<FONT color="green">1575</FONT>    <a name="line.1575"></a>
<FONT color="green">1576</FONT>                }<a name="line.1576"></a>
<FONT color="green">1577</FONT>            }<a name="line.1577"></a>
<FONT color="green">1578</FONT>    <a name="line.1578"></a>
<FONT color="green">1579</FONT>            // apply function composition<a name="line.1579"></a>
<FONT color="green">1580</FONT>            compose(operand, operandOffset, function, result, resultOffset);<a name="line.1580"></a>
<FONT color="green">1581</FONT>    <a name="line.1581"></a>
<FONT color="green">1582</FONT>        }<a name="line.1582"></a>
<FONT color="green">1583</FONT>    <a name="line.1583"></a>
<FONT color="green">1584</FONT>        /** Compute inverse hyperbolic sine of a derivative structure.<a name="line.1584"></a>
<FONT color="green">1585</FONT>         * @param operand array holding the operand<a name="line.1585"></a>
<FONT color="green">1586</FONT>         * @param operandOffset offset of the operand in its array<a name="line.1586"></a>
<FONT color="green">1587</FONT>         * @param result array where result must be stored (for<a name="line.1587"></a>
<FONT color="green">1588</FONT>         * inverse hyperbolic sine the result array &lt;em&gt;cannot&lt;/em&gt; be the input<a name="line.1588"></a>
<FONT color="green">1589</FONT>         * array)<a name="line.1589"></a>
<FONT color="green">1590</FONT>         * @param resultOffset offset of the result in its array<a name="line.1590"></a>
<FONT color="green">1591</FONT>         */<a name="line.1591"></a>
<FONT color="green">1592</FONT>        public void asinh(final double[] operand, final int operandOffset,<a name="line.1592"></a>
<FONT color="green">1593</FONT>                         final double[] result, final int resultOffset) {<a name="line.1593"></a>
<FONT color="green">1594</FONT>    <a name="line.1594"></a>
<FONT color="green">1595</FONT>            // create the function value and derivatives<a name="line.1595"></a>
<FONT color="green">1596</FONT>            double[] function = new double[1 + order];<a name="line.1596"></a>
<FONT color="green">1597</FONT>            final double x = operand[operandOffset];<a name="line.1597"></a>
<FONT color="green">1598</FONT>            function[0] = FastMath.asinh(x);<a name="line.1598"></a>
<FONT color="green">1599</FONT>            if (order &gt; 0) {<a name="line.1599"></a>
<FONT color="green">1600</FONT>                // the nth order derivative of asinh has the form:<a name="line.1600"></a>
<FONT color="green">1601</FONT>                // dn(asinh(x)/dxn = P_n(x) / [x^2 + 1]^((2n-1)/2)<a name="line.1601"></a>
<FONT color="green">1602</FONT>                // where P_n(x) is a degree n-1 polynomial with same parity as n-1<a name="line.1602"></a>
<FONT color="green">1603</FONT>                // P_1(x) = 1, P_2(x) = -x, P_3(x) = 2x^2 - 1 ...<a name="line.1603"></a>
<FONT color="green">1604</FONT>                // the general recurrence relation for P_n is:<a name="line.1604"></a>
<FONT color="green">1605</FONT>                // P_n(x) = (x^2+1) P_(n-1)'(x) - (2n-3) x P_(n-1)(x)<a name="line.1605"></a>
<FONT color="green">1606</FONT>                // as per polynomial parity, we can store coefficients of both P_(n-1) and P_n in the same array<a name="line.1606"></a>
<FONT color="green">1607</FONT>                final double[] p = new double[order];<a name="line.1607"></a>
<FONT color="green">1608</FONT>                p[0] = 1;<a name="line.1608"></a>
<FONT color="green">1609</FONT>                final double x2    = x * x;<a name="line.1609"></a>
<FONT color="green">1610</FONT>                final double f     = 1.0 / (1 + x2);<a name="line.1610"></a>
<FONT color="green">1611</FONT>                double coeff = FastMath.sqrt(f);<a name="line.1611"></a>
<FONT color="green">1612</FONT>                function[1] = coeff * p[0];<a name="line.1612"></a>
<FONT color="green">1613</FONT>                for (int n = 2; n &lt;= order; ++n) {<a name="line.1613"></a>
<FONT color="green">1614</FONT>    <a name="line.1614"></a>
<FONT color="green">1615</FONT>                    // update and evaluate polynomial P_n(x)<a name="line.1615"></a>
<FONT color="green">1616</FONT>                    double v = 0;<a name="line.1616"></a>
<FONT color="green">1617</FONT>                    p[n - 1] = (1 - n) * p[n - 2];<a name="line.1617"></a>
<FONT color="green">1618</FONT>                    for (int k = n - 1; k &gt;= 0; k -= 2) {<a name="line.1618"></a>
<FONT color="green">1619</FONT>                        v = v * x2 + p[k];<a name="line.1619"></a>
<FONT color="green">1620</FONT>                        if (k &gt; 2) {<a name="line.1620"></a>
<FONT color="green">1621</FONT>                            p[k - 2] = (k - 1) * p[k - 1] + (k - 2 * n) * p[k - 3];<a name="line.1621"></a>
<FONT color="green">1622</FONT>                        } else if (k == 2) {<a name="line.1622"></a>
<FONT color="green">1623</FONT>                            p[0] = p[1];<a name="line.1623"></a>
<FONT color="green">1624</FONT>                        }<a name="line.1624"></a>
<FONT color="green">1625</FONT>                    }<a name="line.1625"></a>
<FONT color="green">1626</FONT>                    if ((n &amp; 0x1) == 0) {<a name="line.1626"></a>
<FONT color="green">1627</FONT>                        v *= x;<a name="line.1627"></a>
<FONT color="green">1628</FONT>                    }<a name="line.1628"></a>
<FONT color="green">1629</FONT>    <a name="line.1629"></a>
<FONT color="green">1630</FONT>                    coeff *= f;<a name="line.1630"></a>
<FONT color="green">1631</FONT>                    function[n] = coeff * v;<a name="line.1631"></a>
<FONT color="green">1632</FONT>    <a name="line.1632"></a>
<FONT color="green">1633</FONT>                }<a name="line.1633"></a>
<FONT color="green">1634</FONT>            }<a name="line.1634"></a>
<FONT color="green">1635</FONT>    <a name="line.1635"></a>
<FONT color="green">1636</FONT>            // apply function composition<a name="line.1636"></a>
<FONT color="green">1637</FONT>            compose(operand, operandOffset, function, result, resultOffset);<a name="line.1637"></a>
<FONT color="green">1638</FONT>    <a name="line.1638"></a>
<FONT color="green">1639</FONT>        }<a name="line.1639"></a>
<FONT color="green">1640</FONT>    <a name="line.1640"></a>
<FONT color="green">1641</FONT>        /** Compute inverse hyperbolic tangent of a derivative structure.<a name="line.1641"></a>
<FONT color="green">1642</FONT>         * @param operand array holding the operand<a name="line.1642"></a>
<FONT color="green">1643</FONT>         * @param operandOffset offset of the operand in its array<a name="line.1643"></a>
<FONT color="green">1644</FONT>         * @param result array where result must be stored (for<a name="line.1644"></a>
<FONT color="green">1645</FONT>         * inverse hyperbolic tangent the result array &lt;em&gt;cannot&lt;/em&gt; be the input<a name="line.1645"></a>
<FONT color="green">1646</FONT>         * array)<a name="line.1646"></a>
<FONT color="green">1647</FONT>         * @param resultOffset offset of the result in its array<a name="line.1647"></a>
<FONT color="green">1648</FONT>         */<a name="line.1648"></a>
<FONT color="green">1649</FONT>        public void atanh(final double[] operand, final int operandOffset,<a name="line.1649"></a>
<FONT color="green">1650</FONT>                          final double[] result, final int resultOffset) {<a name="line.1650"></a>
<FONT color="green">1651</FONT>    <a name="line.1651"></a>
<FONT color="green">1652</FONT>            // create the function value and derivatives<a name="line.1652"></a>
<FONT color="green">1653</FONT>            double[] function = new double[1 + order];<a name="line.1653"></a>
<FONT color="green">1654</FONT>            final double x = operand[operandOffset];<a name="line.1654"></a>
<FONT color="green">1655</FONT>            function[0] = FastMath.atanh(x);<a name="line.1655"></a>
<FONT color="green">1656</FONT>            if (order &gt; 0) {<a name="line.1656"></a>
<FONT color="green">1657</FONT>                // the nth order derivative of atanh has the form:<a name="line.1657"></a>
<FONT color="green">1658</FONT>                // dn(atanh(x)/dxn = Q_n(x) / (1 - x^2)^n<a name="line.1658"></a>
<FONT color="green">1659</FONT>                // where Q_n(x) is a degree n-1 polynomial with same parity as n-1<a name="line.1659"></a>
<FONT color="green">1660</FONT>                // Q_1(x) = 1, Q_2(x) = 2x, Q_3(x) = 6x^2 + 2 ...<a name="line.1660"></a>
<FONT color="green">1661</FONT>                // the general recurrence relation for Q_n is:<a name="line.1661"></a>
<FONT color="green">1662</FONT>                // Q_n(x) = (1-x^2) Q_(n-1)'(x) + 2(n-1) x Q_(n-1)(x)<a name="line.1662"></a>
<FONT color="green">1663</FONT>                // as per polynomial parity, we can store coefficients of both Q_(n-1) and Q_n in the same array<a name="line.1663"></a>
<FONT color="green">1664</FONT>                final double[] q = new double[order];<a name="line.1664"></a>
<FONT color="green">1665</FONT>                q[0] = 1;<a name="line.1665"></a>
<FONT color="green">1666</FONT>                final double x2 = x * x;<a name="line.1666"></a>
<FONT color="green">1667</FONT>                final double f  = 1.0 / (1 - x2);<a name="line.1667"></a>
<FONT color="green">1668</FONT>                double coeff = f;<a name="line.1668"></a>
<FONT color="green">1669</FONT>                function[1] = coeff * q[0];<a name="line.1669"></a>
<FONT color="green">1670</FONT>                for (int n = 2; n &lt;= order; ++n) {<a name="line.1670"></a>
<FONT color="green">1671</FONT>    <a name="line.1671"></a>
<FONT color="green">1672</FONT>                    // update and evaluate polynomial Q_n(x)<a name="line.1672"></a>
<FONT color="green">1673</FONT>                    double v = 0;<a name="line.1673"></a>
<FONT color="green">1674</FONT>                    q[n - 1] = n * q[n - 2];<a name="line.1674"></a>
<FONT color="green">1675</FONT>                    for (int k = n - 1; k &gt;= 0; k -= 2) {<a name="line.1675"></a>
<FONT color="green">1676</FONT>                        v = v * x2 + q[k];<a name="line.1676"></a>
<FONT color="green">1677</FONT>                        if (k &gt; 2) {<a name="line.1677"></a>
<FONT color="green">1678</FONT>                            q[k - 2] = (k - 1) * q[k - 1] + (2 * n - k + 1) * q[k - 3];<a name="line.1678"></a>
<FONT color="green">1679</FONT>                        } else if (k == 2) {<a name="line.1679"></a>
<FONT color="green">1680</FONT>                            q[0] = q[1];<a name="line.1680"></a>
<FONT color="green">1681</FONT>                        }<a name="line.1681"></a>
<FONT color="green">1682</FONT>                    }<a name="line.1682"></a>
<FONT color="green">1683</FONT>                    if ((n &amp; 0x1) == 0) {<a name="line.1683"></a>
<FONT color="green">1684</FONT>                        v *= x;<a name="line.1684"></a>
<FONT color="green">1685</FONT>                    }<a name="line.1685"></a>
<FONT color="green">1686</FONT>    <a name="line.1686"></a>
<FONT color="green">1687</FONT>                    coeff *= f;<a name="line.1687"></a>
<FONT color="green">1688</FONT>                    function[n] = coeff * v;<a name="line.1688"></a>
<FONT color="green">1689</FONT>    <a name="line.1689"></a>
<FONT color="green">1690</FONT>                }<a name="line.1690"></a>
<FONT color="green">1691</FONT>            }<a name="line.1691"></a>
<FONT color="green">1692</FONT>    <a name="line.1692"></a>
<FONT color="green">1693</FONT>            // apply function composition<a name="line.1693"></a>
<FONT color="green">1694</FONT>            compose(operand, operandOffset, function, result, resultOffset);<a name="line.1694"></a>
<FONT color="green">1695</FONT>    <a name="line.1695"></a>
<FONT color="green">1696</FONT>        }<a name="line.1696"></a>
<FONT color="green">1697</FONT>    <a name="line.1697"></a>
<FONT color="green">1698</FONT>        /** Compute composition of a derivative structure by a function.<a name="line.1698"></a>
<FONT color="green">1699</FONT>         * @param operand array holding the operand<a name="line.1699"></a>
<FONT color="green">1700</FONT>         * @param operandOffset offset of the operand in its array<a name="line.1700"></a>
<FONT color="green">1701</FONT>         * @param f array of value and derivatives of the function at<a name="line.1701"></a>
<FONT color="green">1702</FONT>         * the current point (i.e. at {@code operand[operandOffset]}).<a name="line.1702"></a>
<FONT color="green">1703</FONT>         * @param result array where result must be stored (for<a name="line.1703"></a>
<FONT color="green">1704</FONT>         * composition the result array &lt;em&gt;cannot&lt;/em&gt; be the input<a name="line.1704"></a>
<FONT color="green">1705</FONT>         * array)<a name="line.1705"></a>
<FONT color="green">1706</FONT>         * @param resultOffset offset of the result in its array<a name="line.1706"></a>
<FONT color="green">1707</FONT>         */<a name="line.1707"></a>
<FONT color="green">1708</FONT>        public void compose(final double[] operand, final int operandOffset, final double[] f,<a name="line.1708"></a>
<FONT color="green">1709</FONT>                            final double[] result, final int resultOffset) {<a name="line.1709"></a>
<FONT color="green">1710</FONT>            for (int i = 0; i &lt; compIndirection.length; ++i) {<a name="line.1710"></a>
<FONT color="green">1711</FONT>                final int[][] mappingI = compIndirection[i];<a name="line.1711"></a>
<FONT color="green">1712</FONT>                double r = 0;<a name="line.1712"></a>
<FONT color="green">1713</FONT>                for (int j = 0; j &lt; mappingI.length; ++j) {<a name="line.1713"></a>
<FONT color="green">1714</FONT>                    final int[] mappingIJ = mappingI[j];<a name="line.1714"></a>
<FONT color="green">1715</FONT>                    double product = mappingIJ[0] * f[mappingIJ[1]];<a name="line.1715"></a>
<FONT color="green">1716</FONT>                    for (int k = 2; k &lt; mappingIJ.length; ++k) {<a name="line.1716"></a>
<FONT color="green">1717</FONT>                        product *= operand[operandOffset + mappingIJ[k]];<a name="line.1717"></a>
<FONT color="green">1718</FONT>                    }<a name="line.1718"></a>
<FONT color="green">1719</FONT>                    r += product;<a name="line.1719"></a>
<FONT color="green">1720</FONT>                }<a name="line.1720"></a>
<FONT color="green">1721</FONT>                result[resultOffset + i] = r;<a name="line.1721"></a>
<FONT color="green">1722</FONT>            }<a name="line.1722"></a>
<FONT color="green">1723</FONT>        }<a name="line.1723"></a>
<FONT color="green">1724</FONT>    <a name="line.1724"></a>
<FONT color="green">1725</FONT>        /** Evaluate Taylor expansion of a derivative structure.<a name="line.1725"></a>
<FONT color="green">1726</FONT>         * @param ds array holding the derivative structure<a name="line.1726"></a>
<FONT color="green">1727</FONT>         * @param dsOffset offset of the derivative structure in its array<a name="line.1727"></a>
<FONT color="green">1728</FONT>         * @param delta parameters offsets (&amp;Delta;x, &amp;Delta;y, ...)<a name="line.1728"></a>
<FONT color="green">1729</FONT>         * @return value of the Taylor expansion at x + &amp;Delta;x, y + &amp;Delta;y, ...<a name="line.1729"></a>
<FONT color="green">1730</FONT>         */<a name="line.1730"></a>
<FONT color="green">1731</FONT>        public double taylor(final double[] ds, final int dsOffset, final double ... delta) {<a name="line.1731"></a>
<FONT color="green">1732</FONT>            double value = 0;<a name="line.1732"></a>
<FONT color="green">1733</FONT>            for (int i = getSize() - 1; i &gt;= 0; --i) {<a name="line.1733"></a>
<FONT color="green">1734</FONT>                final int[] orders = getPartialDerivativeOrders(i);<a name="line.1734"></a>
<FONT color="green">1735</FONT>                double term = ds[dsOffset + i];<a name="line.1735"></a>
<FONT color="green">1736</FONT>                for (int k = 0; k &lt; orders.length; ++k) {<a name="line.1736"></a>
<FONT color="green">1737</FONT>                    if (orders[k] &gt; 0) {<a name="line.1737"></a>
<FONT color="green">1738</FONT>                        term *= FastMath.pow(delta[k], orders[k]) / ArithmeticUtils.factorial(orders[k]);<a name="line.1738"></a>
<FONT color="green">1739</FONT>                    }<a name="line.1739"></a>
<FONT color="green">1740</FONT>                }<a name="line.1740"></a>
<FONT color="green">1741</FONT>                value += term;<a name="line.1741"></a>
<FONT color="green">1742</FONT>            }<a name="line.1742"></a>
<FONT color="green">1743</FONT>            return value;<a name="line.1743"></a>
<FONT color="green">1744</FONT>        }<a name="line.1744"></a>
<FONT color="green">1745</FONT>    <a name="line.1745"></a>
<FONT color="green">1746</FONT>        /** Check rules set compatibility.<a name="line.1746"></a>
<FONT color="green">1747</FONT>         * @param compiler other compiler to check against instance<a name="line.1747"></a>
<FONT color="green">1748</FONT>         * @exception DimensionMismatchException if number of free parameters or orders are inconsistent<a name="line.1748"></a>
<FONT color="green">1749</FONT>         */<a name="line.1749"></a>
<FONT color="green">1750</FONT>        public void checkCompatibility(final DSCompiler compiler)<a name="line.1750"></a>
<FONT color="green">1751</FONT>                throws DimensionMismatchException {<a name="line.1751"></a>
<FONT color="green">1752</FONT>            if (parameters != compiler.parameters) {<a name="line.1752"></a>
<FONT color="green">1753</FONT>                throw new DimensionMismatchException(parameters, compiler.parameters);<a name="line.1753"></a>
<FONT color="green">1754</FONT>            }<a name="line.1754"></a>
<FONT color="green">1755</FONT>            if (order != compiler.order) {<a name="line.1755"></a>
<FONT color="green">1756</FONT>                throw new DimensionMismatchException(order, compiler.order);<a name="line.1756"></a>
<FONT color="green">1757</FONT>            }<a name="line.1757"></a>
<FONT color="green">1758</FONT>        }<a name="line.1758"></a>
<FONT color="green">1759</FONT>    <a name="line.1759"></a>
<FONT color="green">1760</FONT>    }<a name="line.1760"></a>




























































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